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 Srinivasa Aiyangar Ramanujan (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (December 22, 1887 – April 26, 1920) was a groundbreaking Indian mathematician. A child prodigy, he was largely self-taught in mathematics and never attended a university. Ramanujan mainly worked in analytical number theory and is famous for many summation formulas involving constants such as π, prime numbers and the partition function. Often, his formulas were stated without proof and were only later proven to be true.
LifeBorn in Erode, Tamil Nadu, India, by the age of twelve Ramanujan had mastered trigonometry so completely that he was inventing sophisticated theorems that astonished his teachers. In 1898 he entered the Town High School in Kumbakonam. He published several papers in Indian mathematical journals and later got the interests of leading European mathematicians in his work. A 1913 letter to G. H. Hardy contained a long list of theorems without proof. After some initial skepticism, Hardy replied and invited Ramanujan to England. As an orthodox Brahmin, Ramanujan consulted the astrological data for his journey, because his mother was horrified that he would lose his caste by traveling to foreign shores. A fruitful collaboration, which Hardy described as "the one romantic incident in my life", soon developed. Hardy said of some of Ramanujan's formulas, which he could not understand, that "a single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true, for if they were not true, no one would have had the imagination to invent them." Hardy, a prominent mathematician in his own right, stated in an interview by Paul Erdős that his greatest contribution to mathematics was the discovery of Ramanujan. Plagued by health problems all his life, Ramanujan's condition worsened in England, perhaps exacerbated by the scarcity of vegetarian food during the First World War. He was also diagnosed with tuberculosis (Henderson, 1996) and a severe vitamin deficiency, though a 1994 analysis of Ramanujan's medical records and symptoms by Dr. D.A.B Young concluded that it was much more likely he had hepatic amoebiasis, a parasitic infection of the liver. This is also supported by the fact that Ramanujan spent time in Madras, a coastal city where the disease was widespread. It was a difficult disease to diagnose, but once diagnosed was readily curable (Berndt, 1998). He returned to India in 1919 and died soon after in Kumbakonam. His wife S. Janaki Ammal lived outside Chennai (formerly Madras) until her death in 1994. Janaki had been nine when they were married, a fairly common practice in India at the time. (Henderson, 1996) The Ramanujan conjecture and its roleAlthough there are numerous statements that could bear the name Ramanujan conjecture, there is one in particular that was very influential on later work. That Ramanujan conjecture is an assertion on the size of the coefficients of the tau-function, a typical cusp form in the theory of modular forms. It was finally proved as a consequence of the proof of the Weil conjectures; the reduction step is complicated. Ramanujan's notebooksWhile in India, Ramanujan recorded much of the results of his work in the form of three notebooks of loose leaf paper. Only the results of his work were recorded in the notebooks. This was likely influenced by a number of factors. Since paper was very expensive Ramanujan would do most of his work and perhaps his proofs on slate and then transfer only the results to paper. Using only a slate was common for mathematics students in India at the time. He was also likely to have been influenced by the style of one of the books he had learned much of his advanced mathematics from: G.S. Carr's Synopsis of Pure and Applied Mathematics. It was a book of several thousand results only that Carr used to facilitate his tutoring. Finally it is possible that Ramanujan considered his work to be for himself only and therefore only recorded the results. (Berndt, 1998) The first notebook was 351 pages with 16 somewhat organized chapters and some unorganized material. The second notebook had 256 pages in 21 chapters and 100 unorganized pages, with the third notebook containing 33 unorganized pages. The results in his notebooks inspired numerous papers by later mathematicians trying to prove what he had found. Hardy himself created papers exploring material from Ramanujan's work as did G.N. Watson, B.M. Wilson, and Bruce Berndt. (Berndt, 1998) See alsoFurther reading
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pl:Srinivasa Ramanujan de:Srinivasa Aiyangar Ramanujan eo:Srinivasa Aiyangar RAMANUJAN fr:Srinivasa Ramanujan is:Srinivasa Ramanujan kn:ಶ್ರೀನಿವಾಸ ರಾಮಾನುಜನ್ nl:Srinivasa Aaiyangar Ramanujan ja:シュリニヴァーサ・ラマヌジャン fi:Ramanujan sv:Srinivasa Aaiyangar Ramanujan
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