tag:blogger.com,1999:blog-23522986762616615432024-03-05T10:20:37.566+05:30रामानुजनRaj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-2352298676261661543.post-55416370080096269702016-12-22T17:00:00.000+05:302017-01-01T14:26:01.931+05:30रामानुजन से मेरा पहला परिचय<div dir="ltr" style="text-align: left;" trbidi="on">
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<a class="_58cn" data-ft="{"tn":"*N","type":104}" href="https://www.facebook.com/hashtag/%E0%A4%B0%E0%A4%BE%E0%A4%AE%E0%A4%BE%E0%A4%A8%E0%A5%81%E0%A4%9C%E0%A4%A8?source=feed_text&story_id=1327620480612447"><span class="_5afx"><span class="_58cl _5afz"></span></span></a>रामानुजन से (रामानुजन की जीवनी से) मेरा पहला परिचय कब हुआ - यह ठीक -
ठीक याद करना कठिन है, परन्तु इतना निश्चित है यह घटना शायद पाँच<span class="text_exposed_show">वीं
कक्षा से पहले की है. मैं अपने गाँव के एक दुकान में घर का कुछ सामान
खरीदने गया था, तभी दुकान के डेस्क पर पड़े ढेर सारे रद्दी कागजों के बीच एक
पत्रिका दिखी और मैंने उसमें देखा कि किसी गणितज्ञ की जीवनी थी. मुझे उसे
हासिल करने की उत्सुकता बढ़ गई, परन्तु पता नहीं क्यों नहीं माँग पाया. मन
में इच्छा को दबाकर लौट गया. मुझे दूसरी - तीसरी कक्षा से ही गणित अन्य
विषयों से आसान लगता था. और गणितज्ञ के विषय में मेरी भावना थी कि वह गणित
में सबकुछ जानता है. मैं भी गणितज्ञ बनना चाहता था और इसलिए उस पत्रिका में
रुचि थी. परन्तु अफसोस....उसे हासिल नहीं कर पाया ! समय बीतता गया. मेरे
भैया का एक पुस्तकालय हुआ करता था. एक दिन (शायद दसवीं कक्षा से पहले की
बात है - ठीक से याद नहीं) वे उस पुस्तकालय को साफ-सुथरा करने और पुस्तकों
को पुनः व्यवस्थित करने के लिए मुझे साथ लेकर गए. अचानक एक पत्रिका पर
ध्यान गई. आँखें फटी रह गई और मेरे आश्चर्य और हर्ष की सीमा न रही - यह वही
पत्रिका थी - 1987 के विज्ञान प्रगति का दिसंबर अंक. उसके साथ ही विज्ञान
प्रगति के ढेरों पुराने अंक पड़े थे - प्रत्येक अंक में किसी - न - किसी
गणितज्ञ की जीवनी. परन्तु यह अंक रामानुजन विशेषांक था - जो रामानुजन की
जन्म - शती पर प्रकाशित हुई थी और रामानुजन पर बहुत सारी सामग्री उपलब्ध
थी. इसमें गुणाकर मुले का लेख भी था जिसे इच्छुक पाठक अब राजकमल प्रकाशन
द्वारा प्रकाशित उनकी पुस्तक "संसार के महान गणितज्ञ" में पढ़ सकते हैं.
मैंने उस पत्रिका को लाकर पढ़ा. तभी मुझे पता चला कि रामानुजन एक महान
भारतीय गणितज्ञ और संख्या - सिद्धांत शास्त्री है और उनके कई हजार सूत्र अब
भी गणितज्ञों के समझ से बाहर हैं. ये सभी सूत्र संख्याओं के गुणधर्मों से
संबंधित हैं. मैं अचंभित था कि आखिर इन सूत्रों में है क्या ! मैं समझता था
- संख्या के जो भी गुणधर्म हैं - वे सब भाज्य, अभाज्य, सम, विषम, महत्तम
समापवर्तक, लघुतम समापवर्तक, वर्गमूल इत्यादि के अतिरिक्त क्या हो सकता है.
सीमित ज्ञान के कारण मस्तिष्क को कुछ थाह नहीं मिल रहा था. अतः मैं आगे
संख्या- सिद्धांत ही पढ़ने का संकल्प लिया. यद्यपि इस संकल्प में आग में घी
डालने के लिए और भी कुछ करक थे (अभी बस इतना ही !!!). इसी पत्रिका में
मैंने रामानुजन के नोटबुक के विषय में सुना. मैंने उसे प्राप्त करने के लिए
उत्सुक हो गया. इसी पत्रिका से मुझे पता चला कि यह टाटा मूलभूत अनुसंधान
संस्थान के पुस्तकालय में उपलब्ध है. इसके बाद मैं कुछ कारणों से इन
नोटबुकों को भूल गया. और इन नोटबुकों से मेरा साक्षात्कार तब हुआ जब मैं
2009 में टाटा मूलभूत अनुसंधान संस्थान, अनुप्रयुक्त गणित केंद्र, बंगलुरु
में M.Sc.में प्रवेश लिया. अभी मेरे पास सभी नोटबुक उपलब्ध हैं.</span></div>
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Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com2India20.593684 78.962880000000041-8.6044825 37.654286000000042 49.791850499999995 120.27147400000004tag:blogger.com,1999:blog-2352298676261661543.post-33979446773147234662014-12-21T21:54:00.001+05:302014-12-21T21:55:55.899+05:30रामानुजन – गाथा : चयनित पंक्तियाँ <div dir="ltr" style="text-align: left;" trbidi="on">
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<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 20.0pt; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">रामानुजन </span></b><b><span style="color: #4f6228; font-size: 20.0pt; mso-bidi-language: HI; mso-fareast-font-family: "Times New Roman"; mso-themecolor: accent3; mso-themeshade: 128;">– </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 20.0pt; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">गाथा</span></b></div>
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<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; mso-bidi-language: HI; mso-fareast-font-family: "Times New Roman"; mso-themecolor: accent3; mso-themeshade: 128;">महानतम</span></b><b><span style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; mso-bidi-language: HI; mso-fareast-font-family: "Times New Roman"; mso-themecolor: accent3; mso-themeshade: 128;"> <span lang="HI">भारतीय गणितज्ञ - संख्या -सिद्धांत
शास्त्री श्रीनिवास रामानुजन की १२७वीं जयंती के उपलक्ष्य में सादर समर्पित ! </span></span></b><b><span style="color: #4f6228; font-size: 20.0pt; mso-bidi-language: HI; mso-fareast-font-family: "Times New Roman"; mso-themecolor: accent3; mso-themeshade: 128;"> </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 20.0pt; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;"> </span></b></div>
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<span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">[प्रस्तुत कविता</span><span style="color: #4f6228; font-size: 12.0pt; mso-bidi-language: HI; mso-fareast-font-family: "Times New Roman"; mso-themecolor: accent3; mso-themeshade: 128;">–</span><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अंश अपनी दैनंदिनी (डायरी) </span><span style="color: #4f6228; font-size: 12.0pt; mso-bidi-language: HI; mso-fareast-font-family: "Times New Roman"; mso-themecolor: accent3; mso-themeshade: 128;">“ </span><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">गणिताञ्जलि </span><span style="color: #4f6228; font-size: 12.0pt; mso-bidi-language: HI; mso-fareast-font-family: "Times New Roman"; mso-themecolor: accent3; mso-themeshade: 128;">” </span><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">से उद्धरित है</span><span style="color: #4f6228; font-size: 12.0pt; mso-bidi-language: HI; mso-fareast-font-family: "Times New Roman"; mso-themecolor: accent3; mso-themeshade: 128;">]</span></div>
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<span style="color: #4f6228; font-size: 12.0pt; mso-bidi-language: HI; mso-fareast-font-family: "Times New Roman"; mso-themecolor: accent3; mso-themeshade: 128;"> </span><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;"> </span></div>
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<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">थे
रामानुजन गणितज्ञ ऐसे</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">जिन्हें विश्व समादर देते थे।</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">जिनकी मोहिनी प्रतिभा के आगे सब </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">नतमस्तक हो जाते
थे॥ १ ॥</span></b></div>
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<b><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अंक ही उनकी दुनिया </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अंकों में खोए रहते थे।</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अंक ही उनका ईश्वर</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">उन्हें ही वे पूजते थे॥ २ ॥</span></b></div>
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<b><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">हमारी भारत माता ने </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">कितने रत्नों को जन्म दिया।</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">उन रत्नों ने ज्ञानदीप से </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">विश्व को प्रकाशमान किया॥ ३ ॥</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">ईश्वी सन अठारह सौ सतासी </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">बाईस दिसंबर आया था।</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">चिरस्मरणीय विश्व में सुन्दर </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">क्षण यह बनकर आया था॥ ४ ॥</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">गौरवपूर्ण दिवस यह </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">रामानुजन का अवतार हुआ।</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">गणित के इतिहास में </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">नयी प्रतिभा का आविर्भाव हुआ॥ ५ ॥</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">..........</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">पाँच
वर्ष की उम्र में उसने </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अपना विद्यारम्भ किया ।</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अपनी प्रतिभा से शिक्षकों को </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">,</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">चकित करना शुरू किया॥ १० ॥</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">....................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">गणित
में सर्वप्रथम आना</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">रामानुजन की अभिलाषा थी ।</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अपर प्राइमरी कक्षा की </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">फिर से आई परीक्षा थी ॥ १८ ॥</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
<br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">बयालीस अंक पैंतालीस में से </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अंकगणित में उन्होंने प्राप्त किया ।</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">शत प्रतिशत अंक प्राप्त न कर पाने का </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">भारी पश्चाताप
हुआ ॥ १९ ॥</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">दुखकातर ह्रदय उनका </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">घंटों अश्रुपात किया।</span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;"><br />
</span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">गणित ही उनका जीवन </span><span style="color: #4f6228; mso-themecolor: accent3; mso-themeshade: 128;">, </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">गणित से बड़ा ही प्रेम किया ॥ २० ॥</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">.....................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">प्रथम
शोधपत्र था उनका, नवीन और अत्यंत दुरूह |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">सामान्य
पाठक के लिए वह, न समझा गया अनुकूल ||६८||</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">......................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<br /></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">विश्व
को उनकी प्रतिभा का, अब जाकर आभास हुआ |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">कई
गणितज्ञों से उनका सार्थक पत्राचार हुआ ||८४||</span></b></div>
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<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">.....................</span></b></div>
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<br /></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">सन
तेरह में जनवरी सोलह को हार्डी को प्रथम पत्र लिखा |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">प्रमेयों
से परिपूर्ण वह पत्र, इतिहास में विश्व – प्रसिद्द हुआ ||८८||</span></b></div>
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<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">..............................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">प्रथमतः
हार्डी ने उनके, शोधपत्र को समझा था |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">उनकी
अनोखी प्रतिभा को अपार अलौकिक माना था ||९८||</span></b></div>
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<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">..............................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">ट्रिनिटी
कॉलेज में प्रवेश पाकर कैम्ब्रिज वे चले गये |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अलौकिक
प्रतिभा से सबको, विस्मित वे करने लगे ||११४||</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">............................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अठारह
फरवरी सन अठारह, विश्व आज गौरवान्वित था |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">रॉयल
सोसायटी लंदन ने, अपना फैलो मनोनीत किया था ||१५२||</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">...........................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">मद्रास
विश्विद्यालय ने भी, उनका समुचित सम्मान किया |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">गणित
प्राचार्य का पदविशेष, तत्क्षण उनके लिए सृजित किया ||१५८||</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">..........................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">भारत
की प्रतिभा, भारत की काया, इंग्लैंड उनके प्रतिकूल था |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">ठंडी
जलवायु, गिरती सेहत, लौटना भारत श्रेयस्कर था ||१६१||</span></b></div>
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<br /></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">उस
शोध – भूमि को छोड़ उन्होनें, भारत प्रस्थान किया |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">वहां
पर अब शोध न कर पाने का, उन्हें अत्यंत खेद हुआ||१६२||</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">............................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">कैसे
होते स्वस्थ? ईश्वर को यह मंजूर न था |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">गणित
– साधना को विराम देना, रामानुजन को मंजूर न था ||१७७||</span></b></div>
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<br /></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अंत
समय भी, मोक थीटा फंक्शन पर काम किया |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">घनिष्ठ
मित्र हार्डी को, उन परिणामों से सूचित किया ||१७८||</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">.........................</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">विकट
संकट में नहीं झुकने वाले, काल को वे पराजित कर न सके |</span></b></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अपने
अनगिनत प्रेमी जन को, वे रोने से न रोक सके ||१८३||</span></b></div>
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<br /></div>
<div align="center" class="MsoNoSpacing" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: center;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">सन
बीस में अप्रील छब्बीस को, वे ब्रह्माण्ड में समा गये |</span></b></div>
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<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">अपनी
स्मृति को वे जनमानस में छोड़ गये ||१८४||</span></b></div>
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Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com1India20.593684 78.962880000000041-8.580994 37.654286000000042 49.768361999999996 120.27147400000004tag:blogger.com,1999:blog-2352298676261661543.post-22932752249303994022012-10-13T20:30:00.000+05:302013-01-27T20:29:43.345+05:30राष्ट्रीय गणित वर्ष <div dir="ltr" style="text-align: left;" trbidi="on">
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<br />
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<b><i><span lang="HI" style="color: #e36c0a; font-family: "Mangal","serif"; font-size: 14.0pt; line-height: 115%; mso-ascii-theme-font: minor-bidi; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-theme-font: minor-bidi; mso-themecolor: accent6; mso-themeshade: 191;">वर्ष २०१२ को राष्ट्रीय गणित वर्ष घोषित किया गया है , इसका क्या उद्देश्य है
?</span></i></b></div>
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<br /></div>
<div class="MsoNormal" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: justify;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">मानव
– इतिहास में गणित का विकास बहुत पहले ही संभवतः एक स्वतंत्र विषय के रूप में हुआ
| गणित के विकास में भारत का महत्वपूर्ण योगदान रहा है और शताब्दियों तक शीर्ष
स्थान पर रहा है | पाँचवी शताब्दी में आर्यभट और उसके बाद ब्रह्मगुप्त भारत के
महान गणितज्ञों में गिने जाते हैं | भारतीय गणित के इतिहास में शून्य और दशमलव
पद्धति का अविष्कार पूरे मानव – इतिहास और गणित के विश्व – इतिहास में सबसे
महत्वपूर्ण स्थान रखता है और संभवतः कोई अन्य आविष्कार भविष्य में इसका स्थान नहीं
ले सकेगा | </span></b><b><span style="color: #4f6228; font-size: 12.0pt; line-height: 115%; mso-bidi-language: HI; mso-themecolor: accent3; mso-themeshade: 128;"></span></b></div>
<div class="MsoNormal" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: justify;">
<span style="font-size: 12.0pt; line-height: 115%;">
<br />
</span><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">आर्यभट के बाद लगभग हजार वर्षों तक
भारतीय गणित विश्व में प्रथम स्थान पर रहा | इस काल में भारत के महान गणितज्ञों
में केरल के माधव अंतिम गणितज्ञ थे | गणितज्ञ माधव ने न्यूटन और लेबनीज से लगभग दो
शताब्दी पूर्व कलन शास्त्र यानि कैलकुलस के मूलभूत सिद्धांतों की खोज की थी | उनका
यह शोध उनके द्वारा स्थापित केरल के एक विद्यालय की चहारदीवारी में ही सिमटकर रह
गया और शेष दुनिया इससे अनभिज्ञ रहा | दुर्भाग्यवश सोलहवीं शताब्दी के मध्य के बाद
इस विद्यालय का अस्तित्व नहीं रहा | इसके बाद उन्नीसवीं शताब्दी तक भारत में गणित
का विकास अवरूद्ध रहा , जब तक कि इस शताब्दी के अंत में महानतम भारतीय गणितज्ञ
श्रीनिवास रामानुजन का अवतरण नहीं हुआ | परंतु रामानुजन के बाद कुछ गिने – चुने
गणितज्ञ ही अंतर्राष्ट्रीय स्तर पर प्रसिद्ध हुए |</span></b></div>
<div class="MsoNormal" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: justify;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;"> </span></b><span style="font-size: 12.0pt; line-height: 115%;">
</span><b><span style="color: #4f6228; font-size: 12.0pt; line-height: 115%; mso-bidi-language: HI; mso-themecolor: accent3; mso-themeshade: 128;"></span></b></div>
<div class="MsoNormal" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: justify;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">हमारा
देश जितना विशाल है , इसकी तुलना में यहाँ विश्वस्तरीय गणितज्ञों की काफी कमी है |
हमारे देश में छात्र उच्चस्तरीय गणित के अध्ययन में बहुत कम ही रूचि दिखाते हैं ,
फलस्वरूप यहाँ गणित का गुणवत्तापूर्ण और समुचित विकास नहीं हो पा रहा है | यहाँ
छात्रों की गलत आम धारणा है कि गणित के क्षेत्र में रोजगार की कोई सम्भावना नहीं
है | यह धारणा कुछ वर्षों पहले तक सही थी , परंतु आज गणित में शोध और शिक्षण के
क्षेत्र में अपार संभावनायें व्याप्त हैं |</span></b></div>
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<br /></div>
<div class="MsoNormal" style="background: #FABF8F; mso-background-themecolor: accent6; mso-background-themetint: 153; text-align: justify;">
<b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;">भारत
में गणित के विकास को प्रोत्साहित करने हेतु यह आवश्यक है कि गणितज्ञ – समुदाय
इसके लिए उपायों और साधनों कि खोज करें जिससे कि</span></b><b><span lang="HI" style="color: #4f6228; font-size: 12.0pt; line-height: 115%; mso-bidi-language: HI; mso-themecolor: accent3; mso-themeshade: 128;"> </span></b><b><span lang="HI" style="color: #4f6228; font-family: "Mangal","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-themecolor: accent3; mso-themeshade: 128;"><span style="mso-spacerun: yes;"> </span>गणित में उच्च
कोटि के शोध और इनके अनुप्रयोग को प्रोत्साहन मिल सके | इसी उद्देश्य हेतु केंद्र
सरकार ने वैज्ञानिक गतिविविधियों को प्रोत्साहित करने हेतु एक नीति बनायी है | इसी
कड़ी को आगे बढ़ाते हुए हमारे वर्तमान प्रधानमंत्री ने २६ दिसंबर २०११ को रामानुजन
जयंती के अवसर पर<span style="mso-spacerun: yes;"> </span>वर्ष २०१२ को “राष्ट्रीय
गणित वर्ष” घोषित किया | इसका उद्देश्य गणित के विकास को प्रोत्साहित करने हेतु हर
संभव प्रयास करना है , विश्वविद्यालयों में मूल्यांकन पद्धति में सुधार लाना हैं ,
प्रतिभाशाली छात्रों को प्रोत्साहित करना है ताकि उन्हें रामानुजन कि तरह
कठिनाइयों का सामना न करना पड़े और वे शोध में अपना महत्वपूर्ण योगदान दे सके |</span></b><b><span style="color: #4f6228; font-size: 12.0pt; line-height: 115%; mso-bidi-language: HI; mso-themecolor: accent3; mso-themeshade: 128;"></span></b></div>
</div>
Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com1Patna, Bihar, India25.61046 85.14166699999998425.495911 84.980305499999986 25.725009 85.303028499999982tag:blogger.com,1999:blog-2352298676261661543.post-11888483085072954902012-02-19T21:00:00.000+05:302012-02-19T23:25:43.089+05:30Indian Postage Stamp on Ramanujan<div dir="ltr" style="text-align: left;" trbidi="on">
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<i><span style="font-size: x-large;"> Indian Postage Stamp on Ramanujan</span></i></div>
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<i><span style="font-size: x-large;"> </span></i></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEickODZssHbR0Z1N2mGD8bILnnTG7dyBWwIcI6wnJ0eTwNl52rtBFCRMRGm8mu6jZ0AjmCXXtHEHHm6LbTCqpifYBVqRm6SVxXKajcwldtIXbIkUsqE86k8o5v1ZMg1VbfEkud-NwarP9ZM/s1600/scan0022%5B4%5D.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="468" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEickODZssHbR0Z1N2mGD8bILnnTG7dyBWwIcI6wnJ0eTwNl52rtBFCRMRGm8mu6jZ0AjmCXXtHEHHm6LbTCqpifYBVqRm6SVxXKajcwldtIXbIkUsqE86k8o5v1ZMg1VbfEkud-NwarP9ZM/s640/scan0022%5B4%5D.jpg" width="640" /></a></td></tr>
<tr style="color: #990000;"><td class="tr-caption" style="text-align: center;"><h5 align="center">
<span style="font-size: small;">India Post issues second time, a postage stamp on S. Ramanujan </span></h5>
<h5 align="center">
<span style="font-size: small;"> </span><span style="font-size: small;">Date of Issue : 26 December 2011</span></h5>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic0Y0YI6HA3V01HJ_2FMjldv2-ufMBTWoWchSfiboUagAdhyphenhyphen_0j_LHiqYEj_3xT_3jFclhWZlYxrBXv6nR6vW80JAPeKXb8lGAUaj6sZ5hLvWkwtwC0BfNf22BX7Skw17_jWdpc0XTy7No/s1600/image%5B3%5D.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="553" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic0Y0YI6HA3V01HJ_2FMjldv2-ufMBTWoWchSfiboUagAdhyphenhyphen_0j_LHiqYEj_3xT_3jFclhWZlYxrBXv6nR6vW80JAPeKXb8lGAUaj6sZ5hLvWkwtwC0BfNf22BX7Skw17_jWdpc0XTy7No/s640/image%5B3%5D.png" width="640" /></a></td></tr>
<tr style="color: #990000;"><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;">India Post issued a commemorative postage stamp on 75th Birth Anniversary of Srinivasa Ramanujan on 22 December 1962.</span></td></tr>
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</div>Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com0Bangalore, Karnataka, India12.9715987 77.594562712.724026199999999 77.2787057 13.2191712 77.910419699999991tag:blogger.com,1999:blog-2352298676261661543.post-90528761736090731822012-02-16T03:25:00.001+05:302012-02-17T20:25:25.191+05:30Rediscovering Ramanujan : Interview with Prof. Bruce C. Berndt.<div dir="ltr" style="text-align: left;" trbidi="on">
<h2 style="background-color: orange; font-weight: normal;">
<span style="color: #9a6400; font-family: inherit; font-size: xx-small;"><span style="font-size: x-large;"><b style="color: #cc0000;">Rediscovering Ramanujan</b><span style="color: #cc0000;"> </span></span></span></h2>
<h2 style="background-color: orange; font-weight: normal;">
<span style="color: #9a6400; font-family: inherit; font-size: xx-small;"><span style="font-size: x-large;"><span style="color: #cc0000;"></span></span></span><span style="color: #3d85c6; font-size: small;"><i><b><span style="font-size: small;"><span style="font-weight: normal;">Interview with Prof. Bruce C. Berndt.</span></span></b></i></span></h2>
<h2 style="background-color: orange; font-weight: normal;">
<span style="color: #3d85c6; font-size: small;"><i><b><span style="font-size: small;"><span style="font-weight: normal;"></span></span></b></i><b><i></i></b>Interviewer : Asha Krishnakumar </span></h2>
<div style="background-color: #b6d7a8;">
<br /></div>
<div style="background-color: #b6d7a8; text-align: justify;">
The academic lineage of most eminent scholars can be traced to famous
centres of learning, inspiring teachers or an intellectual milieu, but
Srinivasa Ramanujan, perhaps the greatest of Indian mathematicians, had
none of these advantages. He had just one
year of education in a small college; he was basically self-taught.
Working in isolation for most of his short life of 32 years, he had
little contact with other mathematicians. </div>
<div style="background-color: #b6d7a8; text-align: justify;">
<br /></div>
<div style="background-color: #b6d7a8; text-align: justify;">
"Many people falsely promulgate mystical powers to Ramanujan's
mathematical thinking. It is not true. He has meticulously recorded
every result in his three notebooks," says <b>Dr. Bruce C. Berndt</b>, Professor of Mathematics at the University of Illino
is, whose 20 years of research on the three notebooks has been compiled into five volumes. </div>
<div style="background-color: #b6d7a8;">
<br /></div>
<div style="background-color: #b6d7a8; text-align: justify;">
Between 1903 and 1914, before Ramanujan went to Cambridge, he compiled
3,542 theorems in the notebooks. Most of the time Ramanujan provided
only the results and not the proof. Berndt says: "This is perhaps
because for him paper was unaffordable and so he
worked on a slate and recorded the results in his notebooks without the
proofs, and not because he got the results in a flash." </div>
<div style="background-color: #b6d7a8; text-align: justify;">
<br /></div>
<div style="background-color: #b6d7a8; text-align: justify;">
Berndt is the only person who has proved each of the 3,542 theorems. He
is convinced that nothing "came to" Ramanujan but every step was thought
or worked out and could in all probability be found in the notebooks.
Berndt recalls Ramanujan's well-known i
nteraction with G.H. Hardy. Visiting Ramanujan in a Cambridge hospital
where he was being treated for tuberculosis, Hardy said: "I rode here
today in a taxicab whose number was 1729. This is a dull number."
Ramanujan replied: "No, it is a very interestin
g number; it is the smallest number expressible as a sum of two cubes in
two different ways." Berndt believes that this was no flash of insight,
as is commonly thought. He says that Ramanujan had recorded this result
in one of his notebooks before he cam
e to Cambridge. He says that this instance demonstrated Ramanujan's love
for numbers and their properties. </div>
<div style="background-color: #b6d7a8; text-align: justify;">
<br /></div>
<div style="background-color: #b6d7a8; text-align: justify;">
Although Ramanujan's mathematics may seem archaic by today's standards,
in many respects he was far ahead of his time. While the thrust of 20th
century mathematics has been on building general theories, Ramanujan was
a master in finding particular result
s which are now recognised as providing the core for the theories. His
results opened up vistas for further research not only in mathematics
but in other disciplines such as physics, computer science and
statistics. </div>
<div style="background-color: #b6d7a8; text-align: justify;">
<br /></div>
<div style="background-color: #b6d7a8; text-align: justify;">
After Ramanujan's death in 1920, the three notebooks and a sheaf of
papers that he left behind were handed over to the University of Madras.
They were sent to G.N. Watson who, along with B.M. Wilson, edited
sections of the notebooks. After Watson's death
in 1965, the papers, which contained results compiled by Ramanujan
after his return to India from Cambridge in 1914, were handed over to
Trinity College, Cambridge. In 1976, G. E. Andrews of Pennsylvania State
University rediscovered the papers at the T
rinity College Library. Since then these papers have been called
Ramanujan's "lost notebook". According to Berndt, the lost notebook
caused as much stir in the mathematical world as Beethoven's Tenth
Symphony did in the world of Western classical music. </div>
<div style="background-color: #b6d7a8; text-align: justify;">
<br /></div>
<div style="background-color: #b6d7a8; text-align: justify;">
Berndt says that the "unique circumstances surrounding Ramanujan and his
mathematics" make it very difficult to assess his greatness among such
mathematical giants as Newton, Gauss, Euler and Reimann. According to
Berndt, Hardy had provided the following
assessment of his contemporary mathematicians on a scale of 0 to 100:
"On the basis of pure talent he gave himself a rating of 25, his
collaborator J. E. Littlewood 30, German mathematician D. Hilbert 80,
and Ramanujan 100." Berndt says that it is not R
amanujan's greatness but only its measure that is in doubt. </div>
<div style="background-color: #b6d7a8;">
<br /></div>
<div style="background-color: #b6d7a8;">
<br /></div>
<div style="background-color: #b6d7a8; text-align: justify;">
Besides the five volumes, Berndt has written over 100 papers on
Ramanujan's works. He has guided a number of research students in this
area. He now works on Ramanujan's "lost notebook" and on some other
manuscripts and fragments of notes. Recently in Che
nnai to give lectures on Ramanujan's works at the Indian Institute of
Technology, the Institute of Mathematical Sciences and the Ramanujan
Museum and Mathematical Centre, Berndt spoke to <b>Asha Krishnakumar</b>
on his work on Ramanujan's notebooks, the
broad areas in mathematics that Ramanujan had covered, the vistas his
work has opened up and the application of his work in physics,
statistics and communication. </div>
<div style="background-color: #b6d7a8;">
<br /></div>
<div style="background-color: #b6d7a8; color: #cc0000;">
<span style="color: #741b47;">Excerpts from the interview:</span> </div>
<div style="background-color: #ea9999; color: #cc0000;">
<br /></div>
<div style="background-color: #ea9999; color: #741b47;">
<i> <b>How did you get interested in Ramanujan's notebooks?</b></i></div>
<div style="background-color: #ea9999; color: #741b47;">
<i> </i>
</div>
<div style="background-color: #ea9999; color: black; text-align: justify;">
<span style="color: #38761d;">After my Ph.D. at the University of Wisconsin, I took my first position
at the University of Glasgow (Scotland) in 1966-67. Prof. R. A. Rankin
was a leader in number theory at that time. I remember being in Rankin's
office in 1967 when he told me about Ramanujan's notebooks for the first time. He said: "I have a copy of the
notebooks published by the Tata Institute of Fundamental Research,
Bombay (Mumbai). Would you be interested in looking at it?" I said, "No,
I am not interested in it."</span></div>
<div style="background-color: #ea9999; color: #38761d;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
I did not think about the notebooks for some years until early 1974 when
I was on leave at the Institute for Advanced Studies in Princeton, U.S.
In February that year, I was reading two papers of Emil Grosswald in
which he proves some formulae from Ramanujan's notebooks. I realised I could prove these formulae as well by
using a theorem I proved two years ago. I did that and then I was
curious to find out whether there were other formulae in the notebooks
that I could prove using my methods. So, I went
to the Princeton University library and got hold of Ramanujan's
notebooks published by the TIFR. I was thrilled to find out that I could
actually prove some more formulae. But there were a few thousand others
I could not. </div>
<div style="background-color: #ea9999; color: #38761d;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
I was fascinated with the notebooks and in the next few years I wrote
papers around the formulae I had proved from the notebooks. The first
was a repository paper on Ramanujan's theta 2n+1 formula, for which I
did a lot of historical research on other pr
oofs of the formula. This I wrote for a special volume called Srinivasa
Ramanujan's Memorial Volume, published by Jupiter Press in Madras
(Chennai) in 1974. After that, wherever I went, I was all the time
working on, and proving, the various formulae of
Ramanujan's - to be precise - from Chapter 14 of the second notebook.
Then I wrote a sequel to this. </div>
<div style="background-color: #ea9999; color: #38761d;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
Let me jump ahead to May 1977, when I decided to try and prove all the
formulae in Chapter 14. I took this on as a challenge. There were in all
87 results in this chapter. I worked on this for the next one year. I
took the help of my first Ph.D. student,
Ron Evans. </div>
<div style="background-color: #ea9999; color: #38761d;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
After about a year of working on this, the famous mathematician George
E. Andrews visited Illinois and told me that he discovered in the spring
of 1976 Ramanujan's "lost notebook" along with G. N. Watson and B. M.
Wilson's edited volumes on Ramanujan's t
hree notebooks and some of their unpublished notes in the Trinity
College Library. I then got photocopies of Ramanujan's lost notebook and
all the notes of Watson and Wilson. And so I went to the beginning of
the second notebook.</div>
<div style="background-color: #ea9999;">
<br /></div>
<div style="background-color: #ea9999; color: #741b47;">
<b><i>What does the second notebook contain?</i></b></div>
<div style="background-color: #ea9999; color: #741b47;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
This is the main notebook because it is the revised and enlarged version
of the first. I went back to the beginning and went about working my
way through it using Watson and Wilson's notes when necessary. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<div style="color: #741b47;">
<b><i>How long did you work on the second notebook?</i></b></div>
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
I really do not know how many years exactly. But some time in the early 1980s Walter Kaufmann-Buhler, the mathematics editor of <i>Springer Verlag</i> in New York, showed interest in my work and decided to publish it. That had not occurred to me till the
n. I agreed and signed a contract with Springers. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
That was when I started preparing the results with a view to publishing
them. I finally came out with five volumes; I had thought it would be
three. It also took a much longer time than I had anticipated. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
After I completed 21 chapters of the second notebook, the 100 pages of
unorganised material in the second notebook and the 33 pages in the
third had a lot more material. I also found more material in the first
which was not there in the second. So, I fou
nd a lot of new material. It was 20 years before I eventually completed
all the three notebooks. </div>
<div style="background-color: #ea9999;">
<br /></div>
<div style="background-color: #ea9999; color: #741b47;">
<b><i>Why did you start with the second notebook and not the first?</i></b></div>
<div style="background-color: #ea9999;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
I knew that the second was the revised and enlarged edition of the
first. The first was in a rough form and the second, I was relatively
certain, had most of the things that were there in the first and a lot
more. </div>
<div style="background-color: #ea9999;">
<i><br /></i></div>
<div style="background-color: #ea9999; color: #741b47;">
<b><i>What did each notebook contain?</i></b></div>
<div style="background-color: #ea9999; color: #741b47;">
<br /></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="color: #38761d;">The new results that were in the second notebook were generally among
the unorganised pages of the first. And the third notebook was all
unorganised. A higher percentage of the results in the unorganised parts
of the second and the third were new. In oth
er words, you got a higher percentage of new results as you went into
the unorganised material.
</span></div>
<div style="color: #38761d;">
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #741b47;">
<i> <b>What do you mean by new results?</b></i></div>
<div style="background-color: #ea9999; color: #741b47;">
<i><b> </b></i>
</div>
<div style="background-color: #ea9999;">
<span style="color: #38761d;">Results that have not been got earlier. </span></div>
<div style="background-color: #ea9999;">
<br /></div>
<div style="background-color: #ea9999;">
<i> <b style="color: #741b47;">What is the percentage of new results in the notebooks?</b></i></div>
<div style="background-color: #ea9999; color: #741b47;">
<b><i> </i></b>
</div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="color: #38761d;">Hardy estimated that over two-thirds of the work Ramanujan did in India
was rediscovered. That is much too high. I found that well over half is
new. It is difficult to say precisely. I would say that most results
were new because we also have to consider
that in the meantime, from 1920 until I started doing this work, other
people discovered these things. So, I would say that at least two-thirds
of the material was really new when Ramanujan died.
</span></div>
<div style="background-color: #ea9999;">
<br /></div>
<div style="background-color: #ea9999;">
<br /></div>
<div style="background-color: #ea9999;">
<i> <b style="color: #741b47;">Ramanujan is popularly known as a number theorist. Would you give a
broad idea about the results in his notebooks? What areas of mathematics
do they cover?</b></i></div>
<div style="background-color: #ea9999; color: #741b47;">
<b><i> </i></b>
</div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="color: #38761d;">You are right. To much of the mathematical world and to the public in
general, Ramanujan is known as a number theorist. Hardy was a number
theorist but he was also into analysis. When Ramanujan was at Cambridge
with Hardy, he was naturally influenced by
him (Hardy). And so most of the papers he published while he was in
England were in number theory. His real great discoveries are in
partition functions. </span></div>
<div style="background-color: #ea9999;">
<br /></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="color: #38761d;">Along with Hardy, he found a new area in mathematics called
probabilistic number theory, which is still expanding. Ramanujan also
wrote sequels in highly composite numbers and arithmetical functions.
There are half a dozen or more of these papers that ma
de Ramanujan very famous. They are still very important papers in number
theory. </span></div>
<div style="background-color: #ea9999; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="color: #38761d;">However, the notebooks do not contain much of number theory. It is,
broadly speaking, in analysis. I will try and break that down a little
bit. I would say that the area in which Ramanujan spent most of his
time, more than any other, is in elliptic funct
ions (theta functions), which have strong connections with number
theory. In particular, Chapters 16 to 21 of the second notebook and most
of the unorganised portions of the notebooks are on theta functions.
There is a certain type of theta functions ide
ntity which has applications in other areas of mathematics, particularly
in number theory, called modular equations. Ramanujan devoted an
enormous amount of effort on refining modular equations. </span></div>
<div style="background-color: #ea9999; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="color: #38761d;">Ramanujan is also popular for his approximations to pie. Many of his
approximations came with his work on elliptic functions. Ramanujan
computed what are called class invariants. Even as he discovered them,
they were computed by a German mathematician, H
. Weber, in the late 19th and early 20th centuries. But Ramanujan was
unaware of this. He computed 116 of these invariants which are much more
complicated. These have applications not only in approximations to pie
but in many other areas as well. </span></div>
<div style="background-color: #ea9999; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; text-align: justify;">
<b><i> <span style="color: #741b47;">Have you gone through every one of the 3,254 entries in the three
notebooks and proved each of them, including in the unorganised
material?</span></i></b></div>
<div style="background-color: #ea9999; color: #741b47; text-align: justify;">
<b><i> </i></b>
</div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="color: #38761d;">I have gone through every entry in the notebooks. If a result has
already been proved in the literature, then I just wrote the entry down
and said that proofs can be found in this literature and so on. But I
will also discuss the relevance in history of
the entry.</span></div>
<div style="background-color: #ea9999;">
<br /></div>
<div style="background-color: #ea9999; color: #741b47; text-align: justify;">
<b><i> What are the applications of Ramanujan's discoveries in areas such as physics, communications and computer science?</i></b></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> </i>
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
This is a very difficult question to answer because of the way
mathematics and science work. Mathematics is discovered and it is then
there for others to use. And you do not always know who uses it. But I
have regular contact with some physicists who I know use Ramanujan's work. They find the results very useful in their own
application. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #741b47; text-align: justify;">
<i> <b>What are the areas in physics in which Ramanujan's work is used?</b></i></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> </i>
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
The most famous application in physics is in the area of statistical
mechanics. Among those who I know have used Ramanujan's mathematics
extensively is W. Backster, the well-known physicist from Australia. He
used the famous Rogers-Ramanujan identities in what is called the hard hexagon model to describe the molecular
structure of a thin film. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
Many of Ramanujan's works are used but his asymptotic formulae have
found the most important application; I first wrote this in 1974 from
his notebook.
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
Then there is a particular formula of Ramanujan's involving the
exponential function which has been used many times in statistics and
probability.</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
Ramanujan had a number of conjectures in regard to this
formula and one is still unproven. He made this con
jecture in a problem he submitted to the Indian Mathematical Society.
The asymptotic formula is used, for instance, in the popular problem:
What is the minimum number of people you can have in a room so that the
probability that two share a common birthd
ay is more than half? I think it is 21, 22 or 23. Anyway, this problem
can be generalised to many other types of similar problems. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> <b style="color: #741b47;">Have you looked at the lost notebook?</b></i></div>
<div style="background-color: #ea9999; color: #741b47; text-align: justify;">
<b><i> </i></b>
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
That is what I am working on now with Andrews. It contains about 630
results. About 60 per cent of these are of interest to Andrews. He has
proved most of these results. The other 40 per cent are of great
interest to me as most of them were a continuatio
n of what Ramanujan considered in his other notebooks. So, I began
working on them.</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> <b style="color: #741b47;">What are your experiences of working on Ramanujan's notebooks? Do
you think Ramanujan was a freak or a genius or he had the necessary
motivation to write the notebooks?</b></i></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> </i>
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
I think one has to be really motivated to do the kind of mathematics he
was doing, through either teachers or books. We understand from
Ramanujan's biographers that he was motivated in particular by two
books: S. L. Loney's Plane Trigonometry and Carr's
<i>Synopsis of Elementary Results in Pure Mathematics</i> (which was a
compilation of 5,000 theorems with a few proofs) at the age of 12. How
much his teachers motivated him, we really do not know as nothing about
it has been recorded. Reading these book
s and going through the problems must have aroused the curiosity that he
had and inspired him.
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
He is particularly amazing because he took off from the little bit he
knew and extended it so much in so many directions, leading to so many
new and beautiful results. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i><b style="color: #741b47;">Did you find any results difficult to decipher in any of Ramanujan's notbooks?</b> </i></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> </i>
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
Oh yes. I get stuck all the time. At times I have no idea where these
formulae are coming from. Earlier, Ron Evans, whom I have already
mentioned as having worked on Chapter 14, helped me out a number of
times. There are times I would think of a formula
over for about six months or even a year, not getting anywhere. Even now
there are times when we wonder how Ramanujan was ever led to the
formulae. There has to be some chain of reasoning to lead him to think
that there might be a theorem there. But ofte
n this is missing. To begin with, the formulae look strange but over
time we understand where they fit in and how important they are than
they were previously thought to be.</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> <b style="color: #741b47;">Did you find any serious errors in Ramanujan's notebooks?</b></i></div>
<div style="background-color: #ea9999; color: #741b47; text-align: justify;">
<b><i> </i></b>
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
There are a number of misprints. I did not count the number of serious
mistakes but it is an extremely small number - maybe five or ten out of
over 3,000 results. Considering that Ramanujan did not have any rigorous
training, it is really amazing that he
made so few mistakes. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> <b><span style="color: #741b47;">Are the methods of mathematics teaching today motivating enough to produce geniuses like Ramanujan?</span></b></i></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> </i>
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
Some like G. E. Andrews think that much of the reforms have come about
because students do not study as much. This, along with the advent of
computers, has changed things. A lot of mathematics which can be done by
computations, manipulations and by doing
exercises in high school are now being done using calculators and
computers. And the computer, I do not think, gives any motivation. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
The books on calculus reform (that is now introduced in the U.S.)
include sections on using a computer. To calculate the limit of a
sequence given by a formula, the book says press these numbers, x, y and
z... Then there appears a string of numbers that
get smaller and smaller and then you can see that is tends to zero. But
that does not lead to any understanding as to why they are tending to
zero. So, this reasoning, motivation and understanding of why the
sequence tends to zero is not being taught. I
think that is wrong. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> <b style="color: #741b47;">There seem to be two schools of thought: one which thinks that the
development of concepts and ideas is important and the other, like that
in India, which thinks that development of skills is important in
teaching mathematics. Which do you think is more important?</b></i></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<i> </i>
</div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
I think you cannot have one without the other. Both must be taught. The
tendency in the U.S. is to move away from skills and rely on computers. I
do not think this is correct because if you have the skills and
understanding, then you can see if you have
made an error in punching in the computers. Andrews and I have the
experience of students putting down results that are totally ridiculous
because they have not understood what is going on. They do not even
realise that they made mistakes while punching
in the computers. So, developing skills is absolutely necessary. But on
the other hand if you just go on with the skills and have no
understanding of why you are doing this, you lose the motivation and it
becomes just a mechanical exercise. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
However, even now there is a possibility that geniuses like Ramanujan
will emerge. It is important that once you identify such children, books
and material should be found for them specially. The greatest thing
about number theory in which Ramanujan work
ed is that you can give it to people of all ages to stimulate them.
Number theory has problems that are challenging, that are not too easy,
but yet they are durable and motivating. A foremost mathematician (Atle
Selberg) and a great physicist (Freeman Dy
son) of this century have said that they were motivated by Ramanujan's
number theory when they were in their early teens. </div>
<div style="background-color: #ea9999; color: #38761d; text-align: justify;">
<br /></div>
</div>Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com3tag:blogger.com,1999:blog-2352298676261661543.post-22594809766484668682012-02-09T02:42:00.001+05:302012-02-09T02:44:45.422+05:30Srinivasa Ramanujan: A Remarkable Mathematical Genius<div dir="ltr" style="text-align: left;" trbidi="on">
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<tr valign="top"><td align="center" class="heading" style="background-color: orange; color: blue;" valign="middle" width="364"><b>Srinivasa Ramanujan<br />
A Remarkable Mathematical Genius</b></td>
<td align="right" class="heading" style="background-color: orange;" valign="bottom" width="300"></td>
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<td class="VerdanaMedium" style="background-color: #ffd966; color: #3d85c6;" valign="top"><div align="right">
<i><b>By: Dr
Subodh Mahanti </b></i></div>
</td>
</tr>
<tr>
<td class="VerdanaMedium" style="background-color: #f4cccc;" valign="top" width="17%"><img height="197" src="http://www.vigyanprasar.gov.in/scientists/ramanujan1.jpg" width="140" /></td>
<td bgcolor="#f0d2e1" class="VerdanaMedium" style="background-color: #f4cccc;" valign="top" width="83%"><div align="right">
<div align="justify">
Ramanujan’s brief life and death are symbolic
of conditions in India. Of our millions how few get any education
at all; how many live on the verge of starvation. </div>
</div>
<div align="right">
<b>Jawaharlal Nehru in his Discovery of India
</b></div>
<div align="justify">
<br />
Sheer intuitive brilliance coupled to long, hard hours on his slate
made up for most of his educational lapse. This ‘poor and
solitary Hindu pitting his brains against the accumulated wisdom
of Europe’ as Hardy called him, had rediscovered a century
of mathematics and made new discoveries that would captivate mathematicians
for next century. </div>
<div align="right">
<b>Robert Kanigel in The Man who Knew Infinity
: A Life of the Genius Ramanujan</b> </div>
</td>
</tr>
<tr bgcolor="#f0d2e1">
<td class="VerdanaMedium" colspan="2" valign="top"><div style="background-color: orange;">
<br /></div>
<div style="background-color: orange;">
<br /></div>
<div style="background-color: orange;">
I still say to myself when I am depressed and find myself forced
to listen to pompous and tiresome people, ‘Well, I have done
one thing you could never have done, and that is to have collaborated
with both Littlewood and Ramanujan on something like equal terms’.
</div>
<div align="right" style="background-color: orange;">
<b>Godfrey Harold Hardy</b> </div>
<div align="justify" style="background-color: orange;">
“Ramanujan’s life”, as Robert
Kanigel, the author of a marvellous biography of Ramanujan, wrote,
“can be made to serve as parable for almost any lesson you
want to draw from it.” Ramanujan’s example stirred the
imagination of many–particularly that of mathematicians. Thus,
Subrahmanyan Chandrasekhar (1910-95), the Indian born astrophysicist,
who got Nobel Prize in 1983, said : “I think it is fair to
say that almost all the mathematicians who reached distinction during
the three or four decades following Ramanujan were directly or indirectly
inspired by his example.” Even those who do not know about
Ramanujan’s work are bound to be fascinated by his life. As
Kanigel wrote: “Few can say much about his work, and yet something
in the story of his struggle for the chance to pursue his work on
his own terms compels the imagination, leaving Ramanujan a symbol
for genius, for the obstacles it faces, for the burden it bears,
for the pleasure it takes in its own existence.” </div>
<div align="right" style="background-color: orange;">
<br />
<b><br /></b></div>
<div align="right" style="background-color: #b6d7a8;">
<div style="background-color: orange;">
<br /></div>
<b><br /></b><br />
<b><br /></b><br />
<b><br /></b><br />
<div align="justify" style="color: #274e13;">
Ramanujan’s life is full of strange contrasts.
He had no formal training in mathematics but yet “he was a
natural mathematical genius, in the class of Gauss and Euler.”
Probably Ramanujan’s life has no parallel in the history of
human thought. Godfrey Harold Hardy, (1877-1947), who made it possible
for Ramanujan to go to Cambridge and give formal shape to his works,
said in one of his lectures given at Harvard Universty (which later
came out as a book entitled Ramanujan: Twelve Lectures on Subjects
Suggested by His Life and Work): “I have to form myself, as
I have never really formed before, and try to help you to form,
some of the reasoned estimate of the most romantic figure in the
recent history of mathematics, a man whose career seems full of
paradoxes and contradictions, who defies all cannons by which we
are accustomed to judge one another and about whom all of us will
probably agree in one judgement only, that he was in some sense
a very great mathematician.” </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Srinivasa Ramanujan Iyengar (best known as Srinivasa
Ramanujan) was born on December 22, 1887, in Erode about 400 km
from Chennai, formerly known as Madras where his mother’s
parents lived. After one year he was brought to his father’s
town, Kumbakonam. His parents were K. Srinivasa Iyengar and Komalatammal.
He passed his primary examination in 1897, scoring first in the
district and then he joined the Town High School. In 1904 he entered
Kumbakonam’s Government College as F.A. student. He was awarded
a scholarship. However, after school, Ramanujan’s total concentration
was focussed on mathematics. The result was that his formal education
did not continue for long. He first failed in Kumbakonam’s
Government College. He tried once again in Madras from Pachaiyappa’s
College but he failed again. </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
While at school he came across a book entitled
A Synopsis of Elementary Results in Pure and Applied Mathematics
by George Shoobridge Carr. The title of the book does not reflect
its contents. It was a compilation of about 5000 equations in algebra,
calculus, trigonometry and analytical geometry with abridged demonstrations
of the propositions. Carr had compressed a huge mass of mathematics
that was known in the late nineteenth century within two volumes.
Ramanujan had the first one. It was certainly not a classic. But
it had its positive features. According to Kanigel, “one strength
of Carr’s book was a movement, a flow to the formulas seemingly
laid down one after another in artless profusion that gave the book
a sly seductive logic of its own.” Thisbook had a great influence
on Ramanujan’s career. However, the book itself was not very
great. Thus Hardy wrote about the book: “He (Carr) is now
completely forgotten, even in his college, except in so far as Ramanujan
kept his name alive”. He further continued, “The book
is not in any sense a great one, but Ramanujan made it famous and
there is no doubt it influenced him (Ramanujan) profoundly”.
We do not know how exactly Carr’s book influenced Ramanujan
but it certainly gave him a direction. `It had ignited a burst of
fiercely single-minded intellectual activity’. Carr did not
provide elaborate demonstration or step by step proofs. He simply
gave some hints to proceed in the right way. Ramanujan took it upon
himself to solve all the problems in Carr’s Synopsis. And
as <b>E. H. Neville</b>, an English mathematician, wrote
: “In proving one formula, as he worked through Carr’s
synopsis, he discovered many others, and he began the practice of
compiling a notebook.” Between 1903 and 1914 he had three
notebooks. </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
While Ramanujan made up his mind to pursue mathematics
forgetting everything else but then he had to work under extreme
hardship. He could not even buy enough paper to record the proofs
of his results. Once he said to one of his friends, “when
food is problem, how can I find money for paper? I may require four
reams of paper every month.” In fact Ramanujan was in a very
precarious situation. He had lost his scholarship. He had failed
in examination. What is more, he failed to prove a good tutor in
the subject which he loved most. </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
At this juncture, Ramanujan was helped by R. Ramachandra
Rao, then Collector of Nellore. Ramchandra Rao was educated at Madras
Presidency College and had joined the Provincial Civil Service in
1890. He also served as Secretary of the Indian Mathematical Society
and even contributed solution to problem posed in its Journal. The
Indian Mathematical Society was founded by V. Ramaswami Iyer, a
middle-level Government servant, in 1906. Its Journal put Ramanujan
on the world’s mathematical map. Ramaswami Iyer met Ramanujan
sometime late in 1910. Ramaswami Iyer gave Ramanujan notes of introduction
to his mathematical friends in Chennai (then Madras). One of them
was P.V. Seshu Iyer, who earlier taught Ramanujan at the Government
College. For a short period (14 months) Ramanujan worked as clerk
in the Madras Port Trust which he joined on March 1, 1912. This
job he got with the help of S. Narayana Iyer. </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Ramanujan’s name will always be linked to
<b>Godfrey Harold Hardy</b>, a British mathematician.
It is not because Ramanujan worked with Hardy at Cambridge but it
was Hardy who made it possible for Ramanujan to go to Cambridge.
Hardy, widely recognised as the leading mathematician of his time,
championed pure mathematics and had no interest in applied aspects.
He discovered one of the fundamental results in population genetics
which explains the properties of dominant, and recessive genes in
large mixed population, but he regarded the work as unimportant.</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Encouraged by his well-wishers, Ramanujan, then
25 years old and had no formal education, wrote a letter to Hardy
on January 16, 1913. The letter ran into eleven pages and it was
filled with theorems in divergent series. Ramanujan did not send
proofs for his theorems. He requested Hardy for his advice and to
help getting his results published. Ramanujan wrote : “I beg
to introduce myself to you as a clerk in the Accounts Department
of the Port Trust Office at Madras on a salary of only £ 20
per annum. I have had no university education but I have undergone
the ordinary school course. After leaving school I have been employing
the spare time at my disposal to work at mathematics. I have not
trodden through the conventional regular course which is followed
in a university course, but I am striking out a new path for myself.
I have made a special investigation of divergent series in general
and the results I get are termed by the local mathematicians as
“startling“… I would request you to go through
the enclosed papers. Being poor, if you are convinced that there
is anything of value I would like to have my theorems published.
I have not given the actual investigations nor the expressions that
I get but I have indicated the lines on which I proceed. Being inexperienced
I would very highly value any advice you give me “. The letter
has become an important historical document. In fact, ‘this
letter is one of the most important and exciting mathematical letters
ever written’. At the first glance Hardy was not impressed
with the contents of the letter. So Hardy left it aside and got
himself engaged in his daily routine work. But then he could not
forget about it. In the evening Hardy again started examining the
theorems sent by Ramanujan. He also requested his colleague and
a distinguished mathematician, John Edensor Littlewood (1885-1977)
to come and examine the theorems. After examining closely they realized
the importance of Ramanujan’s work. As C.P. Snow recounted,
‘before mid-night they knew and knew for certain’ that
the writer of the manuscripts was a man of genius’. Everyone
in Cambridge concerned with mathematics came to know about the letter.
Many of them thought `at least another <b>Jacobi </b>in
making had been found out’. <b>Bertrand Arthur William
Russell </b>(1872-1970) wrote to Lady Ottoline Morell. “I
found Hardy and Littlewood in a state of wild excitement because
they believe, they have discovered a second Newton, a Hindu Clerk
in Madras … He wrote to Hardy telling of some results he has
got, which Hardy thinks quite wonderful.”</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Fortunately for Ramanujan, Hardy realised that
the letter was the work of a genius. In the next three months Ramanujan
received another three letters from Hardy. However, in the beginning
Hardy responded cautiously. He wrote on 8 February 1913. To quote
from the letter. “I was exceedingly interested by your letter
and by the theorems which you state. You will however understand
that, before I can judge properly of the value of what you have
done it is essential that I should see proofs of some of your assertions
… I hope very much that you will send me as quickly as possible
at any rate a few of your proofs, and follow this more at your leisure
by more detailed account of your work on primer and divergent series.
It seems to me quite likely that you have done a good deal of work
worth publication; and if you can produce satisfactory demonstration
I should be very glad to do what I can to secure it” <b></b>. </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
In the meantime Hardy started taking steps for
bringing Ramanujan to England. He contacted the Indian Office in
London to this effect. Ramanujan was awarded the first research
scholarship by the Madras University. This was possible by the recommendation
of Gilbert Walker, then Head of the Indian Meteorological Department
in Simla. Gilbert was not a pure mathematician but he was a former
Fellow and mathematical lecturer at Trinity College, Cambridge.
Walker, who was prevailed upon by Francis Spring to look through
Ramanujan’s notebooks wrote to the Registrar of the Madras
University : “The character of the work that I saw impressed
me as comparable in originality with that of a Mathematical Fellow
in a Cambridge College; it appears to lack, however, as might be
expected in the circumstances, the completeness and precision necessary
before the universal validity of the results could be accepted.
I have not specialised in the branches of pure mathematics at which
he worked, and could not therefore form a reliable estimate of his
abilities, which might be of an order to bring him a European reputation.
But it was perfectly clear to me that the University would be justified
in enabling S. Ramanujan for a few years at least to spend the whole
of his time on mathematics without any anxiety as to his livelihood.” </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Ramanujan was not very eager to travel abroad.
In fact he was quite apprehensive. However, many of his well-wishers
prevailed upon him and finally Ramanujan left Madras by S.S. Navesa
on March 17, 1914. Ramanujan reached Cambridge on April 18, 1914.
When Ramanujan reached England he was fully abreast of the recent
developments in his field. This was described by J. R. Newman in
1968: “Ramanujan arrived in England abreast and often ahead
of contemporary mathematical knowledge. Thus, in a lone mighty sweep,
he had succeeded in recreating in his field, through his own unaided
powers, a rich half century of European mathematics. One may doubt
whether so prodigious a feat had ever been accomplished in the history
of thought.”</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Today it is simply futile to speculate about what
would have happened if Ramanujan had not come in contact with Hardy.
It could happen either way. But then Hardy should be given due credit
for recognizing Ramanujan’s originality and helping him to
carry out his work. Hardy himself was very clear about his role.
“Ramanujan was”, Hardy wrote, “my discovery. I
did not invent him — like other great men, he invented himself
— but I was the first really competent person who had the
chance to see some of his work, and I can still remember with satisfaction
that I could recognize at once what I treasure I had found.”</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
It may be noted that before writing to Hardy, Ramanujan
had written to two well-known Cambridge mathematicians viz., H.F.
Baker and E.W. Hobson. But both of them had expressed their inability
to help Ramanujan. </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Ramanujan was awarded the B.A. degree in March
1916 for his work on ‘Highly composite Numbers’ which
was published as a paper in the Journal of the London Mathematical
Society. He was the second Indian to become a Fellow of the Royal
Society in 1918 and he became one of the youngest Fellows in the
entire history of the Royal Society. He was elected “for his
investigation in Elliptic Functions and the Theory of Numbers.”
On 13 October 1918 he was the first Indian to be elected a Fellow
of Trinity College, Cambridge.</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
</div>
<div align="justify" style="color: #274e13;">
Much of Ramanujan’s mathematics comes under
the heading of number theory — a purest realm of mathematics.
The number theory is the abstract study of the structure of number
systems and properties of positive integers. It includes various
theorems about prime numbers (a prime number is an integer greater
than one that has not integral factor). Number theory includes analytic
number theory, originated by<b> Leonhard Euler </b>(1707-89);
geometric theory - which uses such geometrical methods of analysis
as Cartesian co-ordinates, vectors and matrices; and probabilistic
number theory based on probability theory. What Ramanujan did will
be fully understood by a very few. In this connection it is worthwhile
to note what Hardy had to say of the work of pure mathematicians:
“What we do may be small, but it has certain character of
permanence and to have produced anything of the slightest permanent
interest, whether it be a copy of verses or a geometrical theorem,
is to have done something beyond the powers of the vast majority
of men.” In spite of abstract nature of his work Ramanujan
is widely known.</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Ramanujan was a mathematical genius in his own
right on the basis of his work alone. He worked hard like any other
great mathematician. He had no special, unexplained power. As Hardy,
wrote: “I have often been asked whether Ramanujan had any
special secret; whether his methods differed in kind from those
of other mathematicians; whether there was anything really abnormal
in his mode of thought. I cannot answer these questions with any
confidence or conviction; but I do not believe it. My belief that
all mathematicians think, at bottom, in the same kind of way, and
that Ramanujan was no exception.”</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
</div>
<div align="justify" style="color: #274e13;">
Of course, as Hardy observed Ramanujan “combined
a power of generalization, a feeling for form and a capacity for
rapid modification of his hypotheses, that were often really startling,
and made him, in his peculiar field, without a rival in his day.</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
</div>
<div align="justify" style="color: #274e13;">
Here we do not attempt to describe what Ramanujan
achieved. But let us note what Hardy had to say about the importance
of Ramanujan’s work. “Opinions may differ as to the
importance of Ramanujan’s work, the kind of standard by which
it should be judged and the influence which it is likely to have
on the mathematics of the future. It has not the simplicity and
the inevitableness of the greatest work; it would be greater if
it were less strange. One gift it shows which no one will deny—profound
and invincible originality.”</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
</div>
<div align="justify" style="color: #274e13;">
The Norwegian mathematician Atle Selberg, one of
the great number theorists of this century wrote : “Ramanujan’s
recognition of the multiplicative properties of the coefficients
of modular forms that we now refer to as cusp forms and his conjectures
formulated in this connection and their later generalization, have
come to play a more central role in the mathematics of today, serving
as a kind of focus for the attention of quite a large group of the
best mathematicians of our time. Other discoveries like the mock-theta
functions are only in the very early stages of being understood
and no one can yet assess their real importance. So the final verdict
is certainly not in, and it may not be in for a long time, but the
estimates of Ramanujan’s nature in mathematics certainly have
been growing over the years. There is doubt no about that.”</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
</div>
<div align="justify" style="color: #274e13;">
Often people tend to speculate what Ramanujan would
have achieved if he had not died or if his exceptional qualities
were recognised at the very beginning. There are many instances
of such untimely death of gifted persons, or rejection of gifted
persons by the society or the rigid educational system. In mathematics
we may cite the cases of <b>Niels Henrik Abel </b>(1809-29)
and <b>Evarista Galois </b>(1811-32). Abel solved one
of the great mathematical problems of his day - finding a general
solution for a class equations called quintiles. Abel solved the
problem by proving that such a solution was impossible. Galois pioneered
the branch of modern mathematics known as group theory. What is
important is that we should recognise the greatness of such people
and take inspiration from their work. </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Even after more than 80 years of the death of Ramanujan
the situation is not very different as far the rigidity of the education
system. Today also a ‘Ramanujan’ is not likely to get
a chance to pursue his career. This situation remains very much
similar as described by JBS Haldane (1982-1964), a British born
geneticist and philosopher who spent last part of his life in India.
Haldane said : “Today in India Ramanujan could not get even
a lectureship in a rural college because he had no degree. Much
less could he get a post through the Union Public Service Commission.
This fact is a disgrace to India. I am aware that he was offered
a chair in India after becoming a Fellow of the Royal Society. But
it is scandalous that India’s great men should have to wait
for foreign recognition. If Ramanujan’s work had been recognised
in India as early it was in England, he might never have emigrated
and might be alive today. We can cast the blame for Ramanujan’s
non-recognition on the British Raj. We cannot do so when similar
cases occur today...”</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Nehru’s statement given at the beginning
is very much valid even today. And for these very reasons the story
of Ramanujan should be told and retold to our younger people particularly
to those who aspire to do something extraordinary but feel dejected
under the prevailing circumstances. And in this connection it is
worthwhile to remember what <b>Chandrasekhar</b> had to
say: “I can recall the gladness I felt at the assurance that
one brought up under circumstances similar to my own could have
achieved what I could not grasp. The fact that Ramanujan’s
early years were spent in a scientifically sterile atmosphere, that
his life in India was not without hardships that under circumstances
that appeared to most Indians as nothing short of miraculous, he
had gone to Cambridge, supported by eminent mathematicians, and
had returned to India with very assurance that he would be considered,
in time as one of the most original mathematicians of the century
— these facts were enough, more than enough, for aspiring
young Indian students to break their bands of intellectual confinement
and perhaps soar the way what Ramanujan had.</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
"As someone has written “Ramanujan
did mathematics for its own sake, for thrill that he got in seeing
and discovering unusual relationships between various mathematical
objects.” Today Ramanujan’s work has some applications
in particle physics or in the calculation of pi up to a very large
number of decimal places. His work on Rieman’s Zeta Function
has been applied to the pyrometry, the investigations of the temperature
of furnaces. His work on the Partition Numbers resulted in two applications
— new fuels and fabrics like nylons. But then highlighting
the importance of the application side Ramanujan’s work is
really not very important. </div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
Ramanujan died of tuberculosis in Kumbakonam on
April 26, 1920. He was only 32 years old. “It was always maths
... Four days before he died he was scribbling,” said Janaki,
his wife. The untimely death of Ramanujan was most unfortunate particularly
so when we take into account the circumstances under which he died.
As Times Magazine rightly wrote: “There is something peculiarly
sad in the spectacle of genius dying young, dying with the first
sweets of recognition and success tasted, but before the full recognition
of powers that lie within.</div>
<div align="justify" style="color: #274e13;">
<br /></div>
<div align="justify" style="color: #274e13;">
"The only Ramanujan Museum in the country,
founded by Shri P. K. Srinivasan, a mathematics teacher, operates
from March 1993 in the Avvai Academy, Royapuram, Madras. The achievement
of Ramanujan was so great that those who can really grasp the work
of Ramanujan ‘may doubt that so prodigious a feat had ever
been accomplished in the history of thought".</div>
<div align="justify">
<br /></div>
<div align="justify" style="background-color: #b6d7a8; color: #741b47;">
<b>Further Reading </b></div>
<div align="justify" style="background-color: #b6d7a8;">
<ol>
<li style="color: #741b47;"> Ramanujan: Twelve Lectures on the Subjects Suggested by His
Life and Work by G. H. Hardy, Chelsea Publishing Co, New York,
1940. <br />
<br />
</li>
<li style="color: #741b47;"> The Man Who Knew Infinity : A Life of the Genius Ramanujan
by R. Kanigel, Abacus Books, London, 1992. <br />
<br />
</li>
<li style="color: #741b47;"> Ramanujan’s Notebooks (Part I&II) by B.C. Berndt
Springer, New York, 1985-1989. <br />
<br />
</li>
<li style="color: #741b47;"> Ramanujan:The Man and the Mathematician by S.R. Ranganathan,
Asia Publishing House, Bombay, 1967. <br />
<br />
</li>
<li style="color: #741b47;"> Srinivasa Ramanujan : A Mathematical Genius by K. Srinivasa
Rao; East West Books (Madras) Pvt. Ltd. 1998.<br />
<br />
</li>
<li><span style="color: #741b47;"> Srinivasa Ramanujan, Suresh Ram, National Book Trust India,
1989. 7) Ganit Jagater Bismay Ramanujan by Satyabachi Sar, Gyan
Bichitra Prakashani, Agartala, 2000. A well-written book in
Bengali.</span></li>
</ol>
</div>
</div>
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</div>Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com7tag:blogger.com,1999:blog-2352298676261661543.post-1695363586164315552012-01-31T01:00:00.000+05:302012-01-31T12:08:02.949+05:30Two Exams Taken by Ramanujan in India<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="background-color: orange; text-align: justify;">
<i><b><span style="color: #38761d;"> <span style="font-size: x-large;"> </span><span style="font-size: large;"><span style="font-size: small;"> ''On Thursday and Friday, December 3 and 4, of 1903, Srinivasa Ramanujan, who was to become the greatest Indian mathematician in his country’s history, sat for the Matriculation Examination of Madras University . From documents recently found in the Tamil Nadu Archives, we have learned that Ramanujan obtained a Second Class place, permitting him to enter the Government College Kumbakonam in the following year with a scholarship. As is now well known, by the time he entered college, Ramanujan was totally immersed in mathematics and would not study any other subject. He thus failed his exams, except for mathematics, at the end of his first college year and lost his scholarship.'' </span> </span></span></b></i></div>
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</div>
<div style="background-color: orange; color: #0b5394;">
<b><span style="font-size: large;"><span style="font-size: small;">This is an excerpt from the article " <i>Two Exams Taken By Ramanujan In</i> <i>India</i>" by the two authors and mathematicians <i>Bruce C. Berndt</i> and <i>C.A. Reddi</i> in which they have produced the complete account....................! </span></span></b></div>
<div style="background-color: orange; color: #0b5394;">
<b><span style="font-size: large;"><span style="font-size: small;">To see the <span style="font-size: large;"><i>Full Article</i></span>, click on the following link : </span></span></b></div>
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<a href="http://www.google.co.in/url?sa=t&rct=j&q=two+exams+taken+by+ramanujan&source=web&cd=2&ved=0CCoQFjAB&url=http%3A%2F%2Fwww.math.uiuc.edu%2F%7Eberndt%2Farticles%2Fexams.pdf&ei=d-kmT77rIeKyiQejwLyaBA&usg=AFQjCNGMx_FNTydCLrQNK_-0mdvFGOHN2w&sig2=E3ozvPsLeblHKT4yHyN6Qg" target="_blank"><b>TWO EXAMS TAKEN BY RAMANUJAN IN INDIA</b></a></div>
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</div>Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com5tag:blogger.com,1999:blog-2352298676261661543.post-43142938543999802632012-01-01T20:00:00.000+05:302012-02-17T17:08:40.286+05:30PM's Speech on the Ramanujan's Birth Anniversary<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="background-color: orange; color: #274e13;">
<i><span style="font-size: small;"><b>PM's Speech on the Ramanujan's Birth Anniversary</b></span></i><u><i><span style="font-size: small;"><b> </b></span></i></u></div>
<div style="background-color: orange;">
<br /></div>
<div style="background-color: #ea9999; text-align: justify;">
Chennai, Dec 26: The Prime Minister, Dr Manmohan Singh, addressed the
125th Birth Anniversary celebrations of noted mathematician Srinivas
Ramanujan in Chennai today. Following is the text of the Prime
Minister's address:<br />
<br />
"We have gathered here today to celebrate the
life and work of a great son of India and of Tamil Nadu, and one of the
greatest mathematicians the world has seen. It is a pleasure to
participate in this function in the memory of Srinivas Ramanujan, whose
extraordinary genius so very brightly lit up the world of mathematics in
the second decade of the last century. Men and women of such dazzling
brilliance and deep intellect are born but rarely. Indeed, Srinivas
Ramanujan´s genius was ranked by the English mathematician G. H. Hardy
in the same class as giants like Euler, Gauss, Archimedes and Isaac
Newton. While we rightly claim Ramanujan as one of our own, he equally
belonged to all humanity like the other great men and women in any
sphere of human thought. </div>
<div style="background-color: #ea9999; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;">Before I proceed further, let me compliment the Ministry of Human
Resource Development, and my colleague Kapil Sibal, for planning year
long celebrations to mark the 125th birth anniversary of Ramanujan. As a
tribute to the great mathematician, our government has decided to
declare his birthday, that is December 22, as the National Mathematics
Day and the year 2012 as a whole as the National Mathematical Year.
India has a long and glorious tradition of mathematics that we need to
encourage and nurture. I hope these steps will help in providing the
additional impetus to the study of mathematics in our country, apart
from making our people more aware of the work of Ramanujan.</span></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;"> </span><br />
<span style="background-color: #ea9999;">
Mathematics seems to have acquired an independent identity as an
intellectual discipline early on in human history. This identity became
more sharply defined in the second half of the millennium before Christ,
thanks to major developments in Greece. In this period, India too made
great strides in mathematics, though in ways very different from the
Greeks. In the early centuries of the Common Era, India was in fact in
the lead in mathematical developments. Aryabhata in the fifth century,
followed by Brahmagupta in the next are reckoned to be among the
all-time great mathematicians. And we taught the world to think of zero
as a number and the modern way of representing all numbers with 10
symbols. This arguably is the single most important mathematical
development in all human history. </span></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;"> </span><br />
<span style="background-color: #ea9999;">
Indian mathematics remained in the forefront for almost a thousand years
following Aryabhata. The last name in the great mathematicians we
produced in this period is that of Madhava of Kerala. I understand
Madhava had discovered the essentials of Calculus some two centuries
before Newton and Leibnitz. His work however was not known beyond the
school he had created in Kerala. That school unfortunately did not last
beyond the middle of the 16th century. </span></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;"> </span><br />
<span style="background-color: #ea9999;">
Intellectual activity receded into the background in the country for the
next few centuries to revive only in the nineteenth century. In the
early part of the nineteenth century, most of our intellectual energies
were given to humanities and it is towards the end of the century that
India began taking an interest in the sciences. In the second decade of
the 20th century, the country could once again stake a claim to
producing world class mathematics, and that was because of the work of
Srinivasa Ramanujan. Ramanujan came from an economically disadvantaged
background and had but a minimal training in mathematics and yet his
genius overcame formidable difficulties to reach the pinnacle of
greatness. The whole of India is proud of Ramanujam and many an Indian
has been inspired by his shining example. Tamil Nadu of course has a
special claim on him for he was a Tamilian. Along with Sir C. V. Raman
and Subramanyam Chandrashekhar, he is among the three great men of
science and mathematics that Tamil Nadu and India have given to the
world in modern times. </span></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;"> </span><br />
<span style="background-color: #ea9999;">
The story of Ramanujan cannot be told without a mention of the Cambridge
mathematician G. H. Hardy, who was responsible for Ramanujan getting
the recognition that was his legitimate due. The parts that Hardy and
Cambridge, which became Ramanujan´s alma-mater, played in the great
mathematician's development represent the very best of the academic
traditions of the West. The stories of the special relationship between
G.H. Hardy and Ramanujan are a part of the folklore of mathematics.</span></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;"> </span><br />
<span style="background-color: #ea9999;">
The fascinating and inspiring story of Ramanujan needs to be told to the
world. I am, therefore, very happy that the organizers have chosen this
occasion to honour Professor Robert Kanigel who has written an
excellent biography of Ramanujan and I am very happy that he is present
here among us today. I greet you sir, and I understand that yours is a
book that has made Ramanujan well known to the public at large all over
the world, capturing vividly the atmosphere of the early nineteenth
century academic world in that part of the world as well as in Britain. I
am also happy that on this occasion, a new edition of the Notebooks of
Ramanujan is also being released. These are photographic reproductions
of unpublished mathematical work of Ramanujan, written out in his own
hand in a series of notebooks during the days he spent in the city of
Chennai. The originals, I am told are in the University of Madras and I
congratulate the University authority for preserving them in its
archives. </span></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;"> </span><br />
<span style="background-color: #ea9999;">The Government of India sets great store by science and has pursued a
policy of encouraging scientific activities of diverse kinds. Given our
traditions, we naturally attach special importance to mathematics. Since
Ramanujan, a number of mathematicians from the country have
distinguished themselves by performing at very high levels. However, it
is a matter of concern that for a country of our size the number of
competent mathematicians that we have is badly inadequate. Over more
than the last three decades many of our young men and women with a
natural ability in mathematics have not pursued the discipline at
advanced levels. This has also resulted in a decline in the quality of
our mathematics teachers both at the school and college levels. There is
a general perception in our society that the pursuit of mathematics
does not lead to attractive career opportunities. This perception must
change. This perception may have been valid some years ago but today
there are many new career opportunities available to mathematicians, and
the teaching profession itself has become much more attractive in
recent years. </span></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;"> </span><br />
<span style="background-color: #ea9999;">The mathematical community has a duty to find out ways and means to
address the shortage of top quality mathematicians in our country. It
must reach out to the public particularly in the modern context where
mathematics has tremendous influence on every kind of human behaviour.
In many ways, mathematics can be regarded as the mother science. The
Natural Sciences have had a long symbiotic relationship with
mathematics. Life Sciences did not seem to have much use for mathematics
till about a hundred years ago, but lately mathematical interventions
have had a tremendous impact on Biology. Mathematics has also influenced
the study of Social Sciences in a big way. The work of many of the
Nobel Laureates in Economics is highly mathematical. Students, parents
and people at large need to be more aware of these facts so that the
study of mathematics as an academic discipline gains popularity in our
country. I am happy that the activities planned in the National
Mathematical Year would focus on promotion of mathematics at all levels-
from schools to cutting edge research.</span></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;"> </span><br />
<span style="background-color: #ea9999;">The Ramanujan story illustrates the inadequacy of the university
evaluation system in the early decades of the last century while at the
same time it shows that the system displayed enough flexibility to take
care of mavericks like Ramanujan. There have been many reforms since
those days but there would still be talent which would elude proper
evaluation. Our institutions of higher learning, therefore, must be
sensitive to this problem. A genius like Ramanujan would shine bright
even in the most adverse of circumstances, but we should be geared to
encourage and nurture good talent which may not be of the same caliber
as that of Ramanujan.</span></div>
<div style="background-color: #ea9999; text-align: justify;">
<br /></div>
<div style="background-color: #ea9999; text-align: justify;">
<span style="background-color: #ea9999;">Let me end by wishing the National Mathematical Year all success. I
expect the activities initiated during this year would be continued in
the coming years as well, so as to help our country make it to the
forefront of education and research in mathematics. That is my ardent
prayer and with these words I thank you for listening to me patiently. </span></div>
</div>Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com0Bangalore, Karnataka, India12.9715987 77.594562712.724026199999999 77.2787057 13.2191712 77.910419699999991tag:blogger.com,1999:blog-2352298676261661543.post-22415712056485843422011-12-29T17:30:00.000+05:302012-03-06T01:39:47.445+05:30Selected Publications About Ramanujan and His Work<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="background-color: #b6d7a8; font-family: Times,"Times New Roman",serif; font-size: large;"><i><b><br /></b></i></span><ul style="background-color: #b6d7a8; color: #274e13; text-align: left;">
<li>Berndt, Bruce C. "<a class="external text" href="http://www.math.uiuc.edu/%7Eberndt/articles/aachen.pdf" rel="nofollow">An Overview of Ramanujan's Notebooks</a>." <i>Charlemagne and His Heritage: 1200 Years of Civilization and Science in Europe</i>. Ed. P. L. Butzer, W. Oberschelp, and H. Th. Jongen. Turnhout, Belgium: Brepols, 1998. 119–146.</li>
<li>Berndt, Bruce C., and George E. Andrews. <i>Ramanujan's Lost Notebook, Part I</i>. New York: Springer, 2005. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/038725529X">ISBN 0-387-25529-X</a>.</li>
<li>Berndt, Bruce C., and George E. Andrews. <i>Ramanujan's Lost Notebook, Part II</i>. New York: Springer, 2008. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/9780387777658">ISBN 978-0-387-77765-8</a></li>
<li>Berndt, Bruce C., and Robert A. Rankin. <i>Ramanujan: Letters and Commentary.</i> Vol. 9. Providence, Rhode Island: American Mathematical Society, 1995. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0821802879">ISBN 0-8218-0287-9</a>.</li>
<li>Berndt, Bruce C., and Robert A. Rankin. <i>Ramanujan: Essays and Surveys.</i> Vol. 22. Providence, Rhode Island: American Mathematical Society, 2001. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0821826247">ISBN 0-8218-2624-7</a>.</li>
<li>Berndt, Bruce C. <i>Number Theory in the Spirit of Ramanujan</i>. Providence, Rhode Island: <a href="http://en.wikipedia.org/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>, 2006. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0821841785">ISBN 0-8218-4178-5</a>.</li>
<li>Berndt, Bruce C. <i>Ramanujan's Notebooks, Part I</i>. New York: Springer, 1985. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0387961100">ISBN 0-387-96110-0</a>.</li>
<li>Berndt, Bruce C. <i>Ramanujan's Notebooks, Part II</i>. New York: Springer, 1999. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/038796794X">ISBN 0-387-96794-X</a>.</li>
<li>Berndt, Bruce C. <i>Ramanujan's Notebooks, Part III</i>. New York: Springer, 2004. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0387975039">ISBN 0-387-97503-9</a>.</li>
<li>Berndt, Bruce C. <i>Ramanujan's Notebooks, Part IV</i>. New York: Springer, 1993. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0387941096">ISBN 0-387-94109-6</a>.</li>
<li>Berndt, Bruce C. <i>Ramanujan's Notebooks, Part V</i>. New York: Springer, 2005. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0387949410">ISBN 0-387-94941-0</a>.</li>
<li>Hardy, G. H. <i>Ramanujan</i>. New York, Chelsea Pub. Co., 1978. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0828401365">ISBN 0-8284-0136-5</a></li>
<li>Hardy, G. H. <i>Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work</i>. Providence, Rhode Island: American Mathematical Society, 1999. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0821820230">ISBN 0-8218-2023-0</a>.</li>
<li>Henderson, Harry. <i>Modern Mathematicians</i>. New York: Facts on File Inc., 1995. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0816032351">ISBN 0-8160-3235-1</a>.</li>
<li>Kanigel, Robert. <i>The Man Who Knew Infinity: a Life of the Genius Ramanujan</i>. New York: <a href="http://en.wikipedia.org/wiki/Charles_Scribner%27s_Sons" title="Charles Scribner's Sons">Charles Scribner's Sons</a>, 1991. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0684192594">ISBN 0-684-19259-4</a>.</li>
<li><a href="http://en.wikipedia.org/wiki/Gina_Kolata" title="Gina Kolata">Kolata, Gina</a>.
"Remembering a 'Magical Genius'", Science, New Series, Vol. 236, No.
4808 (19 Jun. 1987), pp. 1519–1521, American Association for the
Advancement of Science.</li>
<li><a href="http://en.wikipedia.org/wiki/David_Leavitt" title="David Leavitt">Leavitt, David</a>. <i>The Indian Clerk</i>. London: Bloomsbury, 2007. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/9780747593706">ISBN 978-0-7475-9370-6</a> (paperback).</li>
<li>Narlikar, Jayant V. <i>Scientific Edge: the Indian Scientist From Vedic to Modern Times</i>. New Delhi, India: <a href="http://en.wikipedia.org/wiki/Penguin_Books" title="Penguin Books">Penguin Books</a>, 2003. <a class="internal mw-magiclink-isbn" href="http://en.wikipedia.org/wiki/Special:BookSources/0143030280">ISBN 0-14-303028-0</a>.</li>
<li>T.M.Sankaran. "Srinivasa Ramanujan- Ganitha lokathile
Mahaprathibha", (in Malayalam), 2005, Kerala Sastra Sahithya Parishath,
Kochi.</li>
</ul>
</div>Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com0Bengaluru, Karnataka, India12.9715987 77.594562712.724026199999999 77.2787057 13.2191712 77.910419699999991tag:blogger.com,1999:blog-2352298676261661543.post-23743264938688178252011-12-26T17:30:00.000+05:302012-02-17T08:46:32.699+05:30National Mathematics Day : A Tribute to S. Ramanujan<div dir="ltr" style="text-align: left;" trbidi="on">
<h3 class="post-title entry-title" style="background-color: red;">
<span style="font-size: large;"><span style="color: #274e13;">National Mathematical Year</span> <span style="color: #134f5c;">:</span> <span style="color: #0c343d;"><span style="color: #134f5c;">2012</span></span></span></h3>
<h3 class="post-title entry-title" style="background-color: red;">
<i><span style="font-size: small; font-weight: normal;"><span style="color: #0b5394;">National Mathematics Day : December 22 (Ramanujan's Birthday)</span></span></i></h3>
<div class="separator" style="background-color: #93c47d; clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTZ6xpa2hSP8oZkeugRk6qsZVlyY2AnnGWlyJGRwIt-xptSPj43EPf4jkm0pvxE6qSck_uIVbbBy3dBb301fio3bGouRWqNT220Qj9jOowMulR79pWoM2KoJkKXWyOd9Fl6-sVifmtg8sd/s1600/image%5B10%5D.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTZ6xpa2hSP8oZkeugRk6qsZVlyY2AnnGWlyJGRwIt-xptSPj43EPf4jkm0pvxE6qSck_uIVbbBy3dBb301fio3bGouRWqNT220Qj9jOowMulR79pWoM2KoJkKXWyOd9Fl6-sVifmtg8sd/s320/image%5B10%5D.png" width="234" /></a></div>
<h3 class="post-title entry-title" style="background-color: #93c47d;">
</h3>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>Declaring (on Monday, December 26, 2011) <span style="color: #741b47;">2012</span> as the '<span style="color: #741b47;">National</span> <span style="color: #741b47;">Mathematical year</span>' as a tribute to
maths wizard Srinivasa Ramanujan, Prime Minister Manmohan Singh on
Monday voiced concern over the "badly inadequate" number of competent
mathematicians in the country.</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>He also said that the perception that pursuit of mathematics does not lead to attractive career possibilities "must change."</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>"It is a matter of concern that for a country of our size, the number
of competent mathematicians that we have is badly inadequate", he said
at a function to here mark the <span style="color: #741b47;">125th birth anniversary of Ramanujan</span>.</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #741b47; text-align: justify;">
<b><span style="font-size: small;"><i>Singh also declared December 22, the birthday of Ramanujan, as 'National Mathematics Day.'</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>Students have not pursued mathematics at advanced levels over more
than three decades, which has resulted in a decline in quality of
mathematics teachers at schools and colleges, Singh who is on a two-day
visit to the state, told a galaxy of academics at Madras University.</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>"There is a general perception in our society that the pursuit of
mathematics does not lead to attractive career possibilities. This
perception must change. This perception may have been valid some years
ago, but today there are many new career opportunities available to
mathematics and the teaching perception itself has become much more
attractive in recent years", Singh said.</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>The Prime Minister said the mathematical community has a duty to find
out "ways and means" to address the shortage of top quality
mathematicians and reach out to the public, especially in the modern
context, where mathematics has tremendous influence on every kind of
human endeavour.</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>Noting that the Central government has pursued a policy of
encouraging scientific activities of diverse kinds, the Prime Minister
said, "Given our traditions, we naturally attach special importance to
mathematics...in many ways, mathematics can be regarded as the mother
science".</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>He said Ramanujan overcame formidable difficulties to reach the
pinnacle of greatness, illustrating the inadequacy of University
evaluation system in the early decades of the last century, while at the
same time showing the system displayed enough flexibility to take care
of mavericks like him.</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>"There have been many reforms since those days but there would still
be talent which would elude proper evaluation. Our institutions of
higher learning must be sensitive to this problem."</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>"A genius like Ramanujan would shine bright even in the most adverse
of circumstances, but we should be geared to encourage and nurture good
talent which may not be of the same calibre as that of Ramanujan", Singh
said.</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>Honouring Professor Robert Kanigel, who has written a biography of
Ramanujan, Singh said this book has made Ramanujan well known to the
public at large all over the world.</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>He said the country was proud of Ramanujan and Tamil Nadu has a special claim on him for he was a Tamilian.</i></span></b></div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<br /></div>
<div style="color: #274e13; text-align: justify;">
</div>
<div style="background-color: orange; color: #274e13; text-align: justify;">
<b><span style="font-size: small;"><i>"Along with CV Raman and Subramanyam Chandrashekhar (both Nobel
laureates), he is among the three great men of science and mathematics
that Tamil Nadu and India have given to the world of modern times", he
said. </i></span></b></div>
<h3 class="post-title entry-title" style="background-color: orange; color: #274e13;">
<b><span style="font-size: large;"> </span></b></h3>
</div>Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com2Bangalore, Karnataka, India12.9715987 77.594562712.724026199999999 77.2787057 13.2191712 77.910419699999991tag:blogger.com,1999:blog-2352298676261661543.post-79580267121017815862011-12-22T09:00:00.000+05:302012-03-06T01:27:48.544+05:30Selected Publications by Ramanujan<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="background-color: orange; color: white; font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;">
<span style="font-size: large;"><i><b>Selected Publications by Ramanujan</b></i></span><span style="font-size: large;"><i><b> </b></i></span></div>
<div style="background-color: orange;">
<span class="citation book"> </span></div>
<div style="background-color: orange; color: #38761d;">
<span class="citation book"><span style="color: white;">1.</span> Srinivasa Ramanujan, G. H. Hardy, P. V. Seshu Aiyar, B. M. Wilson, Bruce C. Berndt (2000). <i>Collected Papers of Srinivasa Ramanujan</i>. AMS. <a href="http://en.wikipedia.org/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="http://en.wikipedia.org/wiki/Special:BookSources/0-8218-2076-1" title="Special:BookSources/0-8218-2076-1">0-8218-2076-1</a>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collected+Papers+of+Srinivasa+Ramanujan&rft.aulast=Srinivasa+Ramanujan%2C+G.+H.+Hardy%2C+P.+V.+Seshu+Aiyar%2C+B.+M.+Wilson%2C+Bruce+C.+Berndt&rft.au=Srinivasa+Ramanujan%2C+G.+H.+Hardy%2C+P.+V.+Seshu+Aiyar%2C+B.+M.+Wilson%2C+Bruce+C.+Berndt&rft.date=2000&rft.pub=AMS&rft.isbn=0-8218-2076-1&rfr_id=info:sid/en.wikipedia.org:Srinivasa_Ramanujan"><span style="display: none;"> </span></span> </div>
<div style="background-color: orange; color: #38761d;">
This book was originally published in 1927 after Ramanujan's death.
It contains the 37 papers published in professional journals by
Ramanujan during his lifetime. The third re-print contains additional
commentary by Bruce C. Berndt.</div>
<div style="background-color: orange; color: #38761d;">
<span class="citation book"> </span></div>
<div style="background-color: orange; color: #38761d;">
<span class="citation book"><span style="color: white;">2.</span> S. Ramanujan (1957). <i>Notebooks (2 Volumes)</i>. Bombay: Tata Institute of Fundamental Research.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Notebooks+%282+Volumes%29&rft.aulast=S.+Ramanujan&rft.au=S.+Ramanujan&rft.date=1957&rft.place=Bombay&rft.pub=Tata+Institute+of+Fundamental+Research&rfr_id=info:sid/en.wikipedia.org:Srinivasa_Ramanujan"><span style="display: none;"> </span></span> </div>
<div style="background-color: orange; color: #38761d;">
These books contain photo copies of the original notebooks as written by Ramanujan.</div>
<div style="background-color: orange; color: #38761d;">
<span class="citation book"> </span></div>
<div style="background-color: orange; color: #38761d;">
<span class="citation book"><span style="color: white;">3. </span>S. Ramanujan (1988). <i>The Lost Notebook and Other Unpublished Papers</i>. New Delhi: Narosa. <a href="http://en.wikipedia.org/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="http://en.wikipedia.org/wiki/Special:BookSources/354018726X" title="Special:BookSources/354018726X">354018726X</a>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Lost+Notebook+and+Other+Unpublished+Papers&rft.aulast=S.+Ramanujan&rft.au=S.+Ramanujan&rft.date=1988&rft.place=New+Delhi&rft.pub=Narosa&rft.isbn=354018726X&rfr_id=info:sid/en.wikipedia.org:Srinivasa_Ramanujan"><span style="display: none;"> </span></span> </div>
<div style="background-color: orange; color: #38761d;">
This book contains photo copies of the pages of the "Lost Notebook".</div>
<div style="background-color: orange; color: #38761d;">
</div>
<div style="background-color: orange; color: #38761d;">
<span style="color: white;">4.</span> <a class="external text" href="http://www.imsc.res.in/%7Erao/ramanujan/collectedpapers/question/qJIMS.htm" rel="nofollow">Problems posed by Ramanujan</a>, Journal of the Indian Mathematical Society.</div>
<div>
<div>
<span style="background-color: yellow;"></span></div>
<div>
<span style="background-color: yellow;"><span style="background-color: orange;"></span><span style="background-color: #ffe599;"></span></span><span class="mw-headline" id="Selected_publications_about_Ramanujan_and_his_work"></span></div>
</div>
</div>Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com0Bengaluru, Karnataka, India12.9715987 77.594562712.724026199999999 77.2787057 13.2191712 77.910419699999991tag:blogger.com,1999:blog-2352298676261661543.post-57478025228497486872011-01-04T03:31:00.000+05:302012-01-31T01:31:49.258+05:30श्रीनिवास रामानुजन<div dir="ltr" style="text-align: left;" trbidi="on">
<h1 class="documentFirstHeading" style="background-color: #6fa8dc; color: #274e13;">
<span class="" id="parent-fieldname-title"> श्रीनिवास रामानुजन </span> </h1>
<div align="left" class="pullquote" style="background-color: #6fa8dc; color: #274e13;">
<dl class="image-inline captioned">
<dt><a href="http://ehindi.hbcse.tifr.res.in/scientist/ramanujan_data/Ramanujanhome.jpg" rel="lightbox"><img alt="ramanujan_home" height="200" src="http://ehindi.hbcse.tifr.res.in/scientist/ramanujan_data/Ramanujanhome.jpg/image_mini" title="ramanujan_home" width="150" /></a></dt>
<dd class="image-caption" style="width: 150px;"><br /></dd></dl>
<span style="font-size: large;">कुंभकोड़म स्थित रामानुजन का निवास</span></div>
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<span style="font-size: large;">महान गणितज्ञ श्रीनिवास रामानुजन का जन्म 22 दिसम्बर 1887 को मद्रास से 400 किमी. दूर दक्षिण-पश्चिम में इरोड नामक एक छोटे से गांव में हुआ था। रामानुजान जब एक वर्ष के थे तभी उनका परिवार कुम्भकोड़म आ गया था रामानुजन के पिता यहाँ एक कपड़ा व्यापारी की दुकान में मुनीम का कार्य करते थे। पाँच वर्ष की आयु में रामानुजन का दाखिला कुम्भकोड़म् के प्राथमिक विद्यालय में करा दिया गया। सन् 1898 में इन्होंने टाउन हाईस्कूल में प्रवेश लिया और सभी विषयों में अच्छा प्रदर्शन किया। यहीं रामानुजन ने जी. एस. कार्र की गणित के परिणामों पर लिखी किताब पढ़ी और इस पुस्तक से प्रभावित होकर स्वयं ही गणित पर कार्य करना प्रारंभ कर दिया।</span></div>
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<span style="font-size: large;">कुम्भकोड़म् के शासकीय महाविद्यालय में अध्ययन के लिए रामानुजन को छात्रवृत्ति मिलती थी परंतु रामानुजन के द्वारा गणित के अलावा दूसरे सभी विषयों की उपेक्षा करने पर उनकी छात्रवृत्ति बंद कर दी गई। सन् 1905 में रामानुजन मद्रास विश्वविद्यालय की प्रवेश परीक्षा में सम्मिलित हुए परंतु गणित को छोड़कर शेष सभी विषयों में वे अनुत्तीर्ण हो गए। सन् 1906 एवं 1907 की प्रवेश परीक्षा का भी यही परिणाम रहा। आगे के वर्षों में रामानुजन केर की पुस्तक को मार्गदर्शक मानते हुए गणित में कार्य करते रहे और अपने परिणामों को लिखते गए जो कि 'नोटबुक' नाम से प्रसिद्ध हुए।</span></div>
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<span style="font-size: large;"> रामानुजन के मित्र रामचंद्र राव (दाएं) एवं नेल्लौर के जिला कलेक्टर एस. नारायण अय्यर (बाएं)</span></div>
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<span style="font-size: large;">सन् 1909 में इनका विवाह हो गया और वे आजीविका के लिए नौकरी खोजने लगे। नौकरी खोजने के दौरान रामानुजन कई प्रभावशाली व्यक्तियों के सम्पर्क में आए। 'इंडियन मेथमेटिकल सोसायटी' के संस्थापकों में से एक रामचंद्र राव भी उन्हीं प्रभावशाली व्यक्तियों में से एक थे। रामानुजन ने रामचंद्र राव के साथ एक वर्ष तक कार्य किया। इसके लिये इन्हें 25 रू. महीना मिलता था। इन्होंने 'इंडियन मेथमेटिकल सोसायटी' की पत्रिका (जर्नल) के लिए प्रश्न एवं उनके हल तैयार करने का कार्य प्रारंभ कर दिया। सन् 1911 में बर्नोली संख्याओं पर प्रस्तुत शोधपत्र से इन्हें बहुत प्रसिद्धि मिली और मद्रास में गणित के विद्वान के रूप में पहचाने जाने लगे। सन् 1912 में रामचंद्र राव की सहायता से मद्रास पोर्ट ट्रस्ट के लेखा विभाग में लिपिक की नौकरी करने लगे। रामानुजन ने गणित में शोध करना जारी रखा और सन् 1913 में इन्होंने जी. एम. हार्डी को पत्र लिखा, साथ में स्वयं के द्वारा खोजे प्रमेयों की एक लम्बी सूची भी भेजी। ये पत्र हार्डी को सुबह नाश्ते के टेबल पर मिले। इस पत्र में किसी अनजान भारतीय द्वारा बहुत सारे बिना उत्पत्ति के प्रमेय लिखे थे, जिनमें से कई प्रमेय हार्डी देख चुके थे। पहली बार देखने पर हार्डी को ये सब बकवास लगा। उन्होंने इस पत्र को एक तरफ रख दिया और अपने कार्यों में लग गए परंतु इस पत्र की वजह से उनका मन अशांत था। इस पत्र में बहुत सारे ऐसे प्रमेय थे जो उन्होंने न कभी देखे और न सोचे थे। उन्हें बार-बार यह लग रहा था कि यह व्यक्ति (रामानुजन) या तो धोखेबाज है या फिर गणित का बहुत बड़ा विद्वान। रात को 9 बजे हार्डी ने अपने एक शिष्य लिटिलवुड के साथ एक बार फिर इन प्रमेयों को देखा और आधी रात तक वे लोग समझ गये कि रामानुजन कोई धोखेबाज नही बल्कि गणित के बहुत बड़े विद्वान हैं, जिनकी प्रतिभा को दुनिया के सामने लाना आवश्यक है। वे अपने साथी लिटिलवुड और पत्नी एलिस के साथ मद्रास जा रहे एक युवा प्राध्यापक नेविल की मदद लेकर रामानुजन के बारे में और जानकारी जुटाने तथा अगर सम्भव हो, उन्हें कैम्ब्रिज बुलाने के लिए तत्पर हो उठते हैं। हार्डी का यह निर्णय एक ऐसा निर्णय था जिसने न केवल उनकी और उनके दोस्तों की बल्कि पूरे गणित-इतिहास की ही धारा बदल डाली।</span></div>
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कैम्ब्रिज विश्वविद्यालय के गणितज्ञ (1) ई. एच. नेविल (2) जी. एच. हार्डी</span></div>
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<span style="font-size: large;">सन् 1913 में हार्डी के पत्र के आधार पर रामानुजन को मद्रास विश्वविद्यालय से छात्रवृत्ति मिलने लगी। अगले वर्ष सन् 1914 में हार्डी ने रामानुजन के लिए केम्ब्रिज के ट्रिनिटी कॉलेज आने की व्यवस्था की। रामानुजन ने गणित में जो कुछ भी किया था वो सब अपने बल पर किया था। रामानुजन को गणित की कुछ शाखाओं का बिलकुल भी ज्ञान नहीं था पर कुछ क्षेत्रों में उनका कोई सानी नहीं था इसलिए हार्डी ने रामानुजन को पढ़ाने का जिम्मा स्वयं लिया। स्वयं हार्डी ने इस बात को स्वीकार किया कि जितना उन्होंने रामानुजन को सिखाया उससे कहीं ज्यादा रामानुजन ने उन्हें सिखाया। सन् 1916 में रामानुजन ने केम्ब्रिज से बी. एस-सी. की उपाधि प्राप्त की। </span></div>
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<span style="font-size: large;">रामानुजन और हार्डी के कार्यों ने शुरू से ही महत्वपूर्ण परिणाम दिये। यद्यपि सन् 1917 से ही रामानुजन बीमार रहने लगे थे और अधिकांश समय बिस्तर पर ही रहते थे। रामानुजन का जन्म ब्राह्मण कुल में हुआ था। वह धर्म-कर्म को मानते थे और कड़ाई से उनका पालन करते थे। रामानुजन शाकाहारी थे और इंग्लैण्ड में रहते समय वह अपना भोजन स्वयं पकाते थे। इंग्लैण्ड की कड़ी सर्दी और उस पर कड़ा परिश्रम। फलस्वरूप रामानुजन का स्वास्थ्य खराब रहने लगा और उनमें तपेदिक के लक्षण दिखाई देने लगे, तो उन्हें अस्पताल में भर्ती कर दिया गया। इधर उनके लेख उच्चकोटि की पत्रिकाओं में प्रकाशित होने लगे थे। सन् 1918 में, एक ही वर्ष में रामानुजन को कैम्ब्रिज फिलोसॉफिकल सोसायटी, रॉयल सोसायटी तथा ट्रिनिटी कॉलेज, कैम्ब्रिज तीनों का फेलो चुन गया। इससे रामानुजन का उत्साह और भी अधिक बढ़ा और वह खोजकार्य में जोर-शोर से जुट गए। सन् 1919 में स्वास्थ बहुत खराब होने की वजह से उन्हें भारत वापस लौटना पड़ा।</span></div>
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<span style="font-size: large;">श्रीनिवास रामानुजन (बीच में), जी. एच. हार्डी (सबसे दाएं) तथा अन्य साथी ट्रिनिटी कॉलेज, कैम्ब्रिज</span></div>
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<span style="font-size: large;">रामानुजन की स्मरण शक्ति गजब की थी। वे विलक्षण प्रतिभा के धनी और एक महान गणितज्ञ थे। एक बहुत ही प्रसिद्ध घटना है। जब रामानुजन अस्पताल में भर्ती थे तो डॉ. हार्डी उन्हें देखने आए। डॉ. हार्डी जिस टैक्सी में आए थे उसका नं. था 1729 । यह संख्या डॉ. हार्डी को अशुभ लगी क्योंकि 1729 = 7 x 13 x 19 और इंग्लैण्ड के लोग 13 को एक अशुभ संख्या मानते हैं। परंतु रामानुजन ने कहा कि यह तो एक अद्भुत संख्या है। यह वह सबसे छोटी संख्या है, जिसे हम दो घन संख्याओं के जोड़ से दो तरीके में व्यक्त कर सकते हैं।</span></div>
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<span style="font-size: large;">1729 = 12<sup>3</sup> + 1<sup>3</sup></span></div>
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<span style="font-size: large;">1729 = 10<sup>3</sup> + 9<sup>3</sup></span></div>
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<span style="font-size: large;"> श्रीनिवास रामानुजन के सम्मान में भारत सरकार द्वारा जारी डाक टिकट</span></div>
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<span style="font-size: large;">इलिनॉय विश्वविद्यालय के गणित के प्रोफेसर ब्रूस सी. बर्नाड्ट ने रामानुजन की तीन पुस्तकों पर 20 वर्षों तक शोध किया और इस शोध का निष्कर्ष पाँच पुस्तकों के संकलन के रूप में प्रकाशित हुआ है। ब्रूस सी. बनोड्ट कहते हैं, "मुझे यह सही नहीं लगता जब लोग रामानुजन की गणितीय प्रतिभा को किसी दैवीय या आध्यात्मिक शक्ति से जोड़ कर देखते हैं। यह मान्यता ठीक नहीं है। उन्होंने बड़ी सावधानी से अपने शोध निष्कर्षों को अपनी पुस्तिकाओं में दर्ज किया है।" सन् 1903 से 1914 के बीच, कैम्ब्रिज जाने से पहले रामानुजन अपनी पुस्तिकाओं में 3,542 प्रमेय लिख चुके थे। उन्होंने ज्यादातर अपने निष्कर्ष ही दिए थे, उनकी उत्पत्ति नहीं दी। शायद इसलिए कि वे कागज खरीदनें में सक्षम नहीं थे और वे अपना कार्य पहले स्लेट पर करते थे। बाद में बिना उपपत्ति दिए उसे पुस्तिका में लिख लेते थे।</span></div>
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<span style="font-size: large;">सन् 1967 में प्रोफेसर ब्रूस सी. बर्नाड्ट को प्रोफेसर आर. ए. रेंकिन ने 'टाटा इंस्टीट्यूट आफ फंडामेंटल रिसर्च बाम्बे (मुम्बई)' द्वारा प्रकाशित 'रामानुजन नोट बुक्स' दिखाई पर उस समय प्रोफेसर बर्नाड्ट की इस पुस्तक में कोई रुचि नहीं थी। सन् 1974 में इन्होनें एमिल ग्रॉसवॉल्ड के दो पत्रों को पढ़ा जिनमें ग्रॉसवॉल्ड ने रामानुजन के कुछ प्रमेयों की उत्पत्तियाँ दी थीं। प्रोफेसर ब्रूस सी. बर्नाड्ट को लगा कि वह भी रामानुजन के प्रमेयों की उत्पत्तियाँ दे सकते हैं और वह 'रामानुजन नोट बुक्स' के बारे में जानने के लिए उत्सुक हो गए। प्रोफेसर बर्नाड्ट प्रिंसटन विश्वविद्यालय गए और वहाँ से 'टाटा इंस्टीट्यूट आफ फंडामेंटल रिसर्च' द्वारा प्रकाशित 'रामानुजन नोट बुक्स' की एक प्रति ले आए। यह देखकर प्रोफेसर बर्नाड्ट रोमांचित हो गए कि वह कुछ और प्रमेयों की उत्पत्ति देने में सक्षम थे परंतु उस पुस्तक में ऐसे हजारों प्रमेय थे जिनकी उत्पत्ति वे नहीं दे सकते थे और इस तरह प्रोफेसर बर्नाड्ट ने अपना पूरा ध्यान रामानुजन की पुस्तकों के शोध में लगा दिया।</span></div>
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<dt><span style="font-size: large;"><a href="http://ehindi.hbcse.tifr.res.in/scientist/ramanujan_data/Bruce.jpg" rel="lightbox"><img alt="Bruce" height="200" src="http://ehindi.hbcse.tifr.res.in/scientist/ramanujan_data/Bruce.jpg/image_mini" title="Bruce" width="161" /></a></span></dt>
<dd class="image-caption" style="width: 161px;"><span style="font-size: large;">Bruce C. Berndt</span></dd></dl>
<span style="font-size: large;"> प्रोफेसर ब्रूस सी. बर्नाड्ट जिन्होनें रामानुजन की तीन पुस्तकों पर 20 वर्षों तक शोध किया</span></div>
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<span style="font-size: large;">सन् 1919 में इंग्लैण्ड से वापस आने के पश्चात् रामानुजन कोदमंडी गाँव में रहने लगे। रामानुजन का अंतिम समय चारपाई पर ही बीता। वे चारपाई पर पेट के बल लेटे-लेटे कागज पर बहुत तेज गति से लिखते रहते थे मानो उनके मस्तिष्क में गणितीय विचारों की आँधी चल रही हो। रामानुजन स्वयं कहते थे कि उनके द्वारा लिखे सभी प्रमेय उनकी कुल देवी नामागिरि की प्रेरणा हैं। भारत लौटने के पश्चात् भी उनके स्वास्थ में कोई सुधार नही हुआ और 26 अप्रैल 1920 को महज 33 वर्ष की अल्प आयु में श्रीनिवास रामानुजन का स्वर्गवास हो गया। आज भी गणितज्ञ रामानुजन की क्षमताओं से हैरान हैं। वे उनके द्वारा दी गई कई प्रमेयों को कम्प्यूटर की मदद से भी नहीं सुलझा पाते जिन्हें रामानुजन एक कागज और पेंसिल की मदद से हल करते थे।</span></div>
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</div>Raj Kumar Mistrihttp://www.blogger.com/profile/09815645852794654478noreply@blogger.com3