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bettermarks »Math Glossary» Ramanujan, Srinivasa
Surname: Srinivasa Ramanujan
Born: 1887 in Erode (South India)
Died: 1920 in Kumbakonam (South India)
Teaching / research areas: Number theory, theory of series and sequences, elliptic integrals, hypergeometric functions
Srinivasa Ramanujan was an Indian mathematician from the Tamil culture and lived from 1887 to 1920. Without any higher mathematical training, he was largely self-taught in learning several thousand formulas, equations and arithmetic sentences. In particular, he had an exceptional knowledge of number theory. A number of results are named after him. Many of his formulas are still awaiting proof.
Srinivasa Ramanujan was born in 1887 in the Tamil city of Erode, in what is now the state of Tamil Nadu in southern India. His mother raised him in the spirit of the Hindu religion. At school, his teachers noticed his exceptional math skills and he earned a reputation as a math prodigy. He taught himself most of it himself. He found mathematical theorems on his own, for example he discovered them as a schoolboy Bernoulli numbers. When he was given a collection of around 5,000 formulas at the age of 16, he worked it out in self-study. Ramanujan was poor, often starved and all his life from poor health and inadequate medical care. Thanks to scholarships, he should be able to continue studying, but since he neglected subjects other than mathematics and did not pass exams, the scholarships were withdrawn from him and he received no formal higher education in mathematics.
Despite almost fatal illnesses and a lack of higher education in mathematics, Ramanujan managed to publish in Indian scientific journals. In 1909, as is customary in his religion and culture, he married a nine-year-old girl. After he finally found a permanent job as an accountant in 1912, he contacted mathematicians from British universities, in particular from Trinity College in Cambridge, by mail. He enclosed his letters with formulas and results he had discovered.
Only one of the professors he had written to, Godfrey Harold Hardy, recognized and appreciated Ramanujan's abilities. Ramanujan's formulas struck him as extraordinary, but he could not understand whether they were correct and asked Ramanujan for evidence. So Hardy tried to get Ramanujan to Cambridge. Ramanujan hesitated, however. Above all, religious concerns stood in the way of traveling from India to England. Eventually Ramanujan consented after his mother had a vision that dispelled her and her son's religious and other doubts.
Once in England, a fruitful, unequal collaboration developed between Ramanujan and Hardy. Ramanujan seemed entirely intuitive, while Hardy naturally sought formal evidence and followed rigorous methods. Hardy, like other mathematicians, was deeply impressed with Ramanujan's abilities. According to Hardy, Ramanujan could only be compared with mathematical geniuses like Euler or Jacobi. Hardy later said that Ramanujan's discovery was his greatest contribution to the development of mathematics and called this discovery "the only romantic incident in my life."
Ramanujan received a number of awards and honors at Cambridge, including a membership in the Royal Society. Nevertheless, Ramanujan did not feel at home in England and had difficulties adapting to life there. He was homesick and became seriously ill several times. Finally he decided to return to India. In 1919, now world famous among mathematicians, he was back with his family in India. There he died a year later, at the age of 32, from an illness, presumably tuberculosis or amoebic dysentery.
In addition to his publications, Ramanujan's scientific work also includes his four notebooks, which are full of formulas. His last notebook was lost and was not rediscovered until 1976 by George Andrews. In total, Ramanujan is said to have discovered and written down almost 4,000 formulas and arithmetic theorems. Ramanujan's way of working - he almost always just wrote down the finished results and renounced evidence - made his investigations difficult to understand and the formulas he left behind a mystery. Some results have been found to be incorrect or incorrect. Many have since been proven or were known to be correct even then. However, no evidence has been found for some formulas and mathematicians are still puzzling over their meaning.
Contributions to mathematics
Ramanujan's contributions to mathematics are in the fields of number theory, theory of series and sequences, elliptic integrals, and hypergeometric functions. He was one of the first to deal with highly composite numbers. The results named after him include the Landau-Ramanujan constant, the Ramanujan-Soldner constant, Ramanujan theta functions, Rogers-Ramanujan Identities, Ramanujan primes, Ramanujan's sum and many more. However, they are little known in German-speaking countries.
In memory of Ramanujan and his achievements in mathematics, the ICTP Ramanujan Prize and the SASTRA Ramanujan Prize have been awarded since 2005. The Ramanujan Journal deals with the areas of Ramanujan's mathematical research.
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