There are two Ramanujan prizes, both of which were first awarded in 2005, and both of which are for 10,000.
The Ramanujan Prize offered by the Shanmugha Arts, Science, Technology and Research Academy (SASTRA) of Thanjavur, Tamil Nadu, India, is awarded annually to a young mathematician (maximum age 32) for an outstanding contribution in an area of mathematics influenced by the Indian mathematician Srinivasa Ramanujan. The prize is awarded at an international conference held on or around December 22nd, Ramanuja’s birthday, in his home town of Kumbakonam.
The prize is designed not only to honor Ramanuja’s memory, but also to encourage young mathematicians to follow his example. The level of the award, at $10,000, should ensure that the prize is regarded as a prestigious one in the mathematical community and that the winner is a worthy follower in Ramanuja’s footsteps.
The age limit of 32 years was set because that was Ramanuja’s age at his death, and the prize seeks to recognise outstanding talent and promise in a mathematician of similar age.
The second award, given by the Abdus Salam International Centre for Theoretical Physics (ICTP), based in Italy, is funded by the Niels Henrik Abel Memorial Fund. The age limit is 45 years, and is for a researcher from a developing country who has conducted outstanding research in any branch of the mathematical sciences, also in a developing country.
Srinivasa Ramanuja was born on December 22nd 1887 and died on 26th April 1920. His father was a shop assistant. He attended local schools in Kumbakonam, Tamil Nadu, and at the age of 11 was lent some books on advanced trigonometry. He had mastered these before he was 14. By the age of 17 he was undertaking complex research and worked out Euler’s constant to 15 decimal places.
He was awarded a scholarship to the Government College in 1904, but his concentration on mathematics led to him neglecting his other studies and he dropped out of college, having to study on his own and rely on friends for financial support. In 1906 he entered a college in Madras, with the aim of gaining a place at the University.
In 1909 he married, but also became seriously ill, taking a long time to recover. In 1911 he published his first paper, on Bernoulli numbers.
In 1913 he won a scholarship to the University of Madras, but news of his work had reached England, and in 1914 he was invited to join Trinity College, Cambridge. He graduated in 1916 with a dissertation on highly composite numbers. However, his health was poor, caused in part by dietary problems, as he was an orthodox Brahmin and he found it difficult to find suitable food in wartime Britain. It is probable that he was suffering from tuberculosis.
In 1918 he was elected to the Royal Society and to a fellowship of the Cambridge Philosophical Society. He returned to India in 1919, but his health gave way once more and he died in the following year.
Ramanujan’s contribution to mathematics was not only reflected in his published papers on number theory, which were remarkable enough, but in the notebooks he compiled, especially during his Cambridge years. More than 4,000 formulas, on 400 written pages, have given later mathematicians a huge amount of theory to work on, especially as the notebooks contain theorems without proofs. In 1976 another notebook turned up, and this is now referred to as Ramanujan’s “Lost Notebook”. What makes this notebook even more remarkable is that it was written by a dying man in the last year of his life, but contains mathematical insights that another man might take a lifetime to discover.
The fact that the notebooks contain very few proofs does not mean that the theorems are unproven. Ramanujan knew the proofs, but did not need to write them down. When he did give a proof it was often incomplete, because he saw no need to write down all the steps. This is partly the result of his incomplete early education, and partly from an ingrained habit of saving scarce paper.
The 2005 SASTRA Ramanujan Prize was awarded jointly to Professors Manjul Bhargava of Princeton University and Kannan Soundararajan of the University of Michigan. Professor Bhargava was given the award for his discovery of higher order composition laws. Professor Soundararajan was recognized for his contributions to several areas of number theory.
The 2005 ICTP Ramanujan Prize went to Marcelo Viana, a professor at the Institute of Pure and Applied Mathematics (IMPA), Brazil, recognizing his outstanding contributions in the field of dynamical systems.
The 2006 SASTRA Prize was awarded to Professor Terence Tao of the University of California at Los Angeles (UCLA) for contributions to number theory, harmonic analysis, representation theory, and partial differential equations.
The 2006 ICTP Prize winner was Ramdorai Sujatha, Associate Professor, School of Mathematics, Tata Institute of Fundamental Research (TIFR), India, for her work on the arithmetic of algebraic varieties and her substantial contributions to non-commutative Iwasawa theory.
The 2007 SASTRA Prize was won by Professor Ben Green, Hershel Smith Professor of Mathematics, Cambridge University, England, for contributions to several important problems in combinatorial additive number theory.
The 2007 ICTP prize went to Jorge Lauret, of the Universidad Nacional de Cordoba, Argentina. The prize is in recognition of his outstanding contributions to differential geometry and group representations.