Srinivasa Iyengar Ramanujan (1887-1920) was a brilliant, self-taught Indian mathematician and genius who made many fundamental contributions to analytic number theory, computational and probabilistic number theory, and special functions.
Born into a poor Brahmin family of Vaishnavite sect on the outskirts of the southern city of Chennai (formerly Madras) in India, Ramanujan was to discover in himself a deep and abiding passion and talent for numbers and mathematics, which expressed itself in many hours of problem solving from textbooks, in particular, a book by one E. H. Carr containing a synopsis of about 5000 problems in algebra, calculus, trigonometry and geometry. From about school age in 1897 his practice of keeping notebooks for his solutions had developed, by his college years from 1904 onwards, into genuine researches in which he independently derived results. Moving from college to college in Chennai without obtaining a degree, all the while continuing his private researches into advanced topics such as divergent series, continued fractions, and Bernoulli numbers, Ramanujan’s mathematical brilliance impressed all around him, and he began to acquire among the educated classes of Chennai the reputation of genius which would eventually propel him to Cambridge in 1914.
His letter of introduction to G. H. Hardy, Professor of Mathematics at Cambridge and the leading English mathematician of his time, on Jan. 13, 1913, written while working as a lowly postal clerk, and containing 10 pages of dense and deep formulae and identities, is one of the most remarkable documents in the history of mathematics and of science. The enormous distance, and the striking contrasts of position, status, race and religion which separated Ramanujan and Hardy could scarcely be greater, but Hardy’s initial skepticism and surprise was converted overnight, upon consultation with his colleague J. E. Littlewood, into a quizzical admiration and awe of the abilities of this lowly Indian clerk who presumed to dictate from afar the results of his private, mostly night-time, researches done on slate. Within a year, Hardy had made the necessary financial and lodging arrangements in Cambridge, as Ramanujan was being groomed in Chennai for his stay in England, and on the 17th of March, 1914, Ramanujan sailed for London.
Arriving at Trinity College in Cambridge in April, 1914, and working under the direction of eminent English number theorists, mainly Hardy, but also to a certain extent J. E. Littlewood, Ramanujan’s work flowered in many fields, in the theory of partitions and additive number theory, multiplicative number theory, continued fractions, and elliptic functions. Particularly important, in the later reappraisal of his work, would be his joint work with Hardy on an asymptotic formulae for the partition function p(n) involving hyperbolic functions. On the 16th of March, 1916 he graduated with a dissertation on highly composite numbers. It was the unstoppable quantity as much as the profound originality and deep intuition of his work which never ceased to amaze Hardy, Littlewood and others, and for his efforts he was rewarded in 1918 with the double honours of election to fellowship of the Royal Society of London, one of the most prestigious bodies of scientists in Europe and the world, and then of Trinity College in Cambridge.
No doubt much more mathematics could have poured from the pen of Ramanujan, but alas it was not to be. His keeping to a strict Brahmin diet and an unforgiving heavy work schedule, together with the harshness of the English winters and wartime conditions in England, and his own moody and phlegmatic temper, inflicted a severe physical and mental toll on his health. Soon after his return to India in 1919, he died at the age of just 32, it is believed, of amoebic hepatitis. Throughout his life, he remained a very simple man who devoted his life to mathematics. It is undoubtedly true that he was a devout Hindu, and he was even heard to remark that his formulae were the result of divine intuition, specifically, the goddess Namagiri of Nammakal. Skeptics and mathematicians interested in his work might dismiss these statements as irrelevant, but there is no doubt that Ramanujan saw divine purpose in his work, and he was no different in this sense from any educated Brahmin of his time. In any case, it is yet another aspect of the “aura of mystery” and enigma which surrounds Ramanujan even today.
The interest in Ramanuan’s work dissipated and his reputation waned, understandably perhaps, after his shockingly premature death, as the principal actors on the stage, Hardy, Littlewood, Watson et. al. found, or had to find, other stimuli. But the memory of Ramanujan never died among the members of Hardy’s circle at Cambridge. Indeed, his work on partitions, hypergeometric series, and special functions would gain renewed worldwide interest with the discoveries of certain “lost” notebooks by the American number theorist George Andrews in 1976. Ultimately, it took a new generation of young mathematicians in the 1980s to look at Ramanujan’s work with fresh eyes, and to raise its estimate in the mathematical community. The single most important event, in this regard, was the Ramanujan Centennial staged in India in 1987. This was followed by the creation of the Ramanujan Journal in 1997. Ramanujan has, in fact, two other journals named after him, the Hardy-Ramanujan Journal, and the Journal of the Ramanujan Mathematical Society, making him the only mathematician to have this unique honour. An important reference for the entire corpus of Ramanujan’s published work also exists now in the form of his collected papers.
Ramanujan’s work has led to important advances in pure number theory, and has found applications in probability, statistical mechanics, and molecular physics, and his mathematical reputation is secure. What is remarkable also is the growth in popular interest in Ramanujan, not just as a mystical number genius but as a man of human interest, as a man whose story is one of brilliance and courage overcoming adversity, a story of universal and perennial appeal. This is best exemplified by the production of two new, imminent biographical motion pictures, the first a film by the duo of British actor Stephen Fry, himself a Cambridge graduate, and Indian filmmaker Dev Benegal, and the second by the American filmmaker Matthew Brown.
Ramanujan lived for and loved numbers and the patterns they make. He saw it as his destiny to tease out these patterns albeit in his own unfathomable, inimitable way. His name is forever associated with the thrill of mathematical discovery, and his work, his example and the adventure of his life will inspire each new generation of researchers, students and ordinary people the world over.
