Srinivasa Aaiyangar Ramanujan [shrinivAsa Aiyangar ramAnadjan] (December 22, 1887 - April 26, 1920) was a famous Indian mathematician.
Ramanujan mainly worked in analytical number theory and is famous for many amazingly deep and beautiful summation formulas involving constants such as &pi, prime numbers and partition function. Often, his formulas were stated without proof and were only later proven to be true.
Born 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 was largely self-taught and never attended university. He published several papers in Indian mathematical journals and then attempted to interest European mathematicians in his work. A 1913 letter to G. H. Hardy contained a long list of theorems without proof; Hardy replied, invited Ramanujan to England and a fruitful collaboration developed. 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.
Hardy said about some 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."
Plagued by health problems all his life, Ramanujan's condition worsened in England, which is said to be due to scarcity of vegetarian food during the First World War. 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, getting only a meagre amount as pension.
Although there are numerous statements that could bear the name 'Ramanujan conjecture', there is one in particular that was very influential on later work.
The 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. This was finally proved as a consequence of the proof of the Weil conjectures. The reduction step wasn't at all simple (work of Michio Kuga and contributions also of Mikio Sato, Goro Shimura and Ihara, followed by Deligne) and the existence of the connection inspired some of the deep work in the late 1960s when the consequences of the etale cohomology theory were being worked out.
The Ramanujan conjecture and its role
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