Srinivasa Aiyangar Ramanujan [srInivAsa aiyangAr rAmAnujan] (December 22, 1887 – April 26, 1920) was a groundbreaking Indian mathematician. A child prodigy, he was largely self-taught in mathematics and never attended university.
Ramanujan mainly worked in analytical number theory and is famous for many summation formulas involving constants such as π, 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 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 scepticism, 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."
Plagued by health problems all his life, Ramanujan's condition worsened in England, perhaps due to the 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.
The Ramanujan conjecture and its role
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 Yasutaka 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 étale cohomology theory were being worked out.