Happy Birthday Sir Srinivasa Ramanujan

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Happy Birthday sir.....

If u were alive for few more years, we could have climbed few more steps in mathematics...




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Despite his academic failure Ramanujan threw himself into the pursuit of new results in mathematics. He worked long and hard. A friend of Ramanujan known as Sandow related the following conversation with Ramanujan:

[i]Sandow[/i]: Ramanju, they all call you a genius.

[i]Ramanujan[/i]: What! Me, a genius! Look at my elbow, it will tell you the story.

[i]Sandow[/i]: What is all this, Ramanju? Why is it so rough and black?

[i]Ramanujan[/i]: My elbow has become rough and black in making a genius of me! Night and day I do my calculations on slate. It is too slow to look for a rag to wipe it with. I wipe the slate almost every few minutes with my elbow.

[i]Sandow[/i]: So, you are a mountain of industry. Why use a slate when you have to do so much calculation? Why not use paper?

[i]Ramanujan[/i]: When food itself is a problem, how can I find money for paper? I may require four reams of paper every month.

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It is one of the most romantic stories in the history of mathematics: in 1913, the English mathematician G. H. Hardy received a strange letter from an unknown clerk in Madras, India. The ten-page letter contained about 120 statements of theorems on infinite series, improper integrals, continued fractions, and number theory (Here is a [url="http://www.usna.edu/Users/math/meh/rama.dvi"].dvi file[/url] with a sample of these results). Every prominent mathematician gets letters from cranks, and at first glance Hardy no doubt put this letter in that class. But something about the formulas made him take a second look, and show it to his collaborator J. E. Littlewood. After a few hours, they concluded that the results "must be true because, if they were not true, no one would have had the imagination to invent them".
Thus was Srinivasa Ramanujan (1887-1920) introduced to the mathematical world. Born in South India, Ramanujan was a promising student, winning academic prizes in high school. But at age 16 his life took a decisive turn after he obtained a book titled [i]A Synopsis of Elementary Results in Pure and Applied Mathematics[/i]. The book was simply a compilation of thousands of mathematical results, most set down with little or no indication of proof. It was in no sense a mathematical classic; rather, it was written as an aid to coaching English mathematics students facing the notoriously difficult Tripos examination, which involved a great deal of wholesale memorization. But in Ramanujan it inspired a burst of feverish mathematical activity, as he worked through the book's results and beyond. Unfortunately, his total immersion in mathematics was disastrous for Ramanujan's academic career: ignoring all his other subjects, he repeatedly failed his college exams.
As a college dropout from a poor family, Ramanujan's position was precarious. He lived off the charity of friends, filling notebooks with mathematical discoveries and seeking patrons to support his work. Finally he met with modest success when the Indian mathematician Ramachandra Rao provided him with first a modest subsidy, and later a clerkship at the Madras Port Trust. During this period Ramanujan had his first paper published, a 17-page work on Bernoulli numbers that appeared in 1911 in the [i]Journal of the Indian Mathematical Society[/i]. Still no one was quite sure if Ramanujan was a real genius or a crank. With the encouragement of friends, he wrote to mathematicians in Cambridge seeking validation of his work. Twice he wrote with no response; on the third try, he found Hardy.
Hardy wrote enthusiastically back to Ramanujan, and Hardy's stamp of approval improved Ramanujan's status almost immediately. Ramanujan was named a research scholar at the University of Madras, receiving double his clerk's salary and required only to submit quarterly reports on his work. But Hardy was determined that Ramanujan be brought to England. Ramanujan's mother resisted at first--high-caste Indians shunned travel to foreign lands--but finally gave in, ostensibly after a vision. In March 1914, Ramanujan boarded a steamer for England.
Ramanujan's arrival at Cambridge was the beginning of a very successful five-year collaboration with Hardy. In some ways the two made an odd pair: Hardy was a great exponent of rigor in analysis, while Ramanujan's results were (as Hardy put it) "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account". Hardy did his best to fill in the gaps in Ramanujan's education without discouraging him. He was amazed by Ramanujan's uncanny formal intuition in manipulating infinite series, continued fractions, and the like: "I have never met his equal, and can compare him only with Euler or Jacobi."
One remarkable result of the Hardy-Ramanujan collaboration was a formula for the number p([i]n[/i]) of partitions of a number [i]n[/i]. A partition of a positive integer [i]n[/i] is just an expression for [i]n[/i] as a sum of positive integers, regardless of order. Thus p(4) = 5 because 4 can be written as 1+1+1+1, 1+1+2, 2+2, 1+3, or 4. The problem of finding p([i]n[/i]) was studied by Euler, who found a formula for the generating function of p([i]n[/i]) (that is, for the infinite series whose [i]n[/i]th term is p([i]n[/i])[i]x[sup]n[/sup][/i]). While this allows one to calculate p([i]n[/i]) recursively, it doesn't lead to an explicit formula. Hardy and Ramanujan came up with such a formula (though they only proved it works asymptotically; Rademacher proved it gives the exact value of p([i]n[/i])).
Ramanujan's years in England were mathematically productive, and he gained the recognition he hoped for. Cambridge granted him a Bachelor of Science degree "by research" in 1916, and he was elected a Fellow of the Royal Society (the first Indian to be so honored) in 1918. But the alien climate and culture took a toll on his health. Ramanujan had always lived in a tropical climate and had his mother (later his wife) to cook for him: now he faced the English winter, and he had to do all his own cooking to adhere to his caste's strict dietary rules. Wartime shortages only made things worse. In 1917 he was hospitalized, his doctors fearing for his life. By late 1918 his health had improved; he returned to India in 1919. But his health failed again, and he died the next year.
Besides his published work, Ramanujan left behind several notebooks, which have been the object of much study. The English mathematician G. N. Watson wrote a long series of papers about them. More recently the American mathematician Bruce C. Berndt has written a multi-volume study of the notebooks. In 1997 [i]The Ramanujan Journal[/i] was launched to publish work "in areas of mathematics influenced by Ramanujan".

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December 22, 2012, marks the 125th anniversary of the birth of legendary Indian mathematician Srinivasa Ramanujan. An intuitive mathematical genius, Ramanujan's discoveries have influenced several areas of mathematics, but he is probably most famous for his contributions to number theory and infinite series, among them fascinating formulas ([url="http://www.carma.newcastle.edu.au/jon/RAMA125f.pdf"] pdf [/url]) that can be used to calculate digits of pi in unusual ways.
Last December Prime Minister Manmohan Singh declared 2012 to be a National Mathematics Year in India in honor of Ramanujan's quasiquicentennial. Ramanujan's story is dramatic and somewhat larger than life. It is even the subject of an opera by Indian-German composer Sandeep Bhagwati, a novel and two plays . Largely self-taught, he dropped out of college, took a job as a clerk in Madras and attracted the attention of British mathematician G. H. Hardy through written correspondence in 1913. Although Ramanujan's mother believed that as a Brahmin (the highest class in the Indian caste system, which was in place at the time) he should not travel overseas, Ramanujan, aged 27, went to England in 1914 and spent the ensuing war years working with Hardy and other mathematicians at the University of Cambridge. He grew quite ill in England, and in 1919 he returned to India where he died in 1920. Since his death at age 32 mathematicians have analyzed his notebooks ([url="http://www.math.uiuc.edu/~berndt/articles/aachen.pdf"]pdf [/url]), which are full of formulas but light on justification. Most of the formulas have turned out to be correct, and researchers continue to learn from his work while trying to understand and prove them.
India's mathematical heritage extends far beyond Ramanujan's time. The nation is considered home of the concept of zero. Babylonians had used a space as a placeholder (similar to the role of "0" in the number 101), but this space could not stand alone or at the end of a number. (In our number system, as in theirs, this could be problematic; imagine trying to tell the difference between the numbers 1 and 10 by context alone.) In India, however, zero was treated as a number like any other. India is also the home of our decimal numeral system.
Indian government and mathematical societies pursued several projects to celebrate their year of mathematics, from enrichment programs for students and teachers to the "Mathematical Panorama Lectures" that occurred around the country. This series of 20 short lecture courses, which will continue into 2013, brings prominent mathematicians from different fields to Indian universities to deliver five or six lectures. M. S. Raghunathan, president of the Ramanujan Mathematical Society and chair of the organizing committee for the National Mathematics Year, wrote in an e-mail that he hopes the lectures will facilitate an infusion of Indian talent into fields that lack it right now.
Indeed, a primary purpose of the year of mathematics is to reinvigorate mathematical education in India. In his speech announcing the event, Prime Minister Singh said that although India has produced many distinguished mathematicians, "for a country of our size, the number of competent mathematicians that we have is badly inadequate." He mentioned concerns about the rigidity of India’s academic system, which some believe might squelch rather than nurture mathematical curiosity and achievement. "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," he said. Singh also mentioned the need to prevent attrition of mathematically interested people. "There is a general perception in our society that the pursuit of mathematics does not lead to attractive career opportunities," he said. "This perception must change." Lectures for undergraduates, camps for motivated youngsters and educational programs designed to acquaint teachers with new topics and pedagogical ideas have all been part of the attempt to nurture mathematical interest at all levels.
Two longer-term projects begun this year could help as well: a documentary on the history of Indian mathematics and a mathematics museum in Chennai. Raghunathan hopes that the documentary will be available in 2014 and the museum will open its doors in 2015.
This yearlong fete is culminating in "The Legacy of Srinivasa Ramanujan," a conference at the University of Delhi from December 17 to 22. Included are technical lectures on mathematics influenced by Ramanujan's work, public presentations on Ramanujan's notebooks, dance performances and a film about Ramanujan's life. The annual SASTRA Ramanujan Prize, which recognizes a mathematician age 32 or younger who works in a field influenced by Ramanujan, will be awarded as well. The awardee this year is Zhiwei Yun of Stanford University, whose work lies at the intersection of geometric representation theory, algebraic geometry and number theory.

[badrii]

baaboi, naaku matha antey picha bhayam,

any way you are great sir.......salute to you........

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Ramanujam garu HBD