ARTLESS INNOCENTS AND IVORY-TOWER SOPHISTICATES:SOME
PERSONALITIES ON THE INDIAN MATHEMATICAL SCENE.
PERSONALITIES ON THE INDIAN MATHEMATICAL SCENE.
BY DR.M.S.RAGHUNATHAN.
At the beginning of the 20th century science was still an esoteric pursuit of reclusive intellectuals. The quiet revolution in the academic worlds of Gottingen, Copenhagen, Cambridge, and Paris of the early decades exploded into global awareness of science with Hiroshima. With Sputnik, science soared even higher in public esteem and many a scientist, became a public figure, a celebrity, an icon for the youth.Physicists dominated this celebrity parade, but there were chemists and biologists in fair number. In this context of hype about science and adulation for the scientist. I think the mathematicians described best by a Tamil proverb: he is the hapless fellow who brought home a coper vessel after taking part in a raid on Kubera's Alakapuri!Many great names in mathematics are entirely unfamiliar to people outside the scientific community. This article is about some mathematicians who have contributed significantly to mathematics in the 20th century and more importantly, have had considerable influence on mathematics in India. Some of them are probably not very well known even within the scientific community.
A word about the choice of personalities that I have made they are all men who figured a good deal in the mathematical lore that I was brought up on at the Tata Insitute of Fundamental Research: and that lore has its bias.
I begin inevitably with Srinivasa Ramanujan, the best known Indian mathematician, who is reckoned among the greatest mathematical intellects of the twentieth century. The romantic story of the passage of the poor clerk in the Madras Port Trust to the portals of the ivory towers of Cambridge and the subsequent tragedy of genius cut-off in its prime by illness is well-known, and so I will not dwell on it.
To many mathematicians , Ramanujan's thought processes have an element of mystery about them . Hardy(who was responsible for Ramanujan becoming known internationally) ,would have none of that, but Littlewood, Hardy's close friend and collaborator certainly thought so. Mark Kac,another famous name, describes him as a "magician rather than a genius." Bruce Berndt, a mathematician who has now spent two decades unraveling Ramanujan's note books, says , and I quote-"I still don't understand it all-I maybe able to prove it, but I do not know where it comes from and where it fits into mathematics." Some of Ramanujan's Indian contemporaries were sure that he was deeply religious and were ready to believe even in divine intervention. 
We may not have a clear idea about the nature of Ramanujan's thoughtprocesses. There is however one trait of his which emerges clearly from contemporary writings about him: he was entirely artless and was modest to a fault: his near total lack of feelings of self importance is indeed striking.He does not seem to have had a true measure of his own extraordinary talents despite Hardy playing " Jambavan to his Hanuman ."
There is in fact the episode of his attempted suicide in England that suggests periods of somewhat fragile self-esteem. It happened when the depression caused by his illness was compounded by family problems and Trinity's racist rejection of his nomination to its Fellowship ( Trinity did appoint him a Fellow later.) Ramanujan threw himself before a train , but luckily a guard brought the train to a halt in time.To prevent his arrest for attempted suicide, Hardy attempted some white lies ; he told the police that Ramanujan was a Fellow of the Royal Society ( at that point of time Ramanujan was only a candidate ; he was elected a month later ) and that Fellows of the Royal Society could not be arrested ( which was of course nonsense ). The Police were not taken in , but nvertheless did not press the charge.
There is in fact the episode of his attempted suicide in England that suggests periods of somewhat fragile self-esteem. It happened when the depression caused by his illness was compounded by family problems and Trinity's racist rejection of his nomination to its Fellowship ( Trinity did appoint him a Fellow later.) Ramanujan threw himself before a train , but luckily a guard brought the train to a halt in time.To prevent his arrest for attempted suicide, Hardy attempted some white lies ; he told the police that Ramanujan was a Fellow of the Royal Society ( at that point of time Ramanujan was only a candidate ; he was elected a month later ) and that Fellows of the Royal Society could not be arrested ( which was of course nonsense ). The Police were not taken in , but nvertheless did not press the charge.Ramanujan's insights continue to influence mathematical developments to this day. His collected works have been a source of inspiration to many outstanding mathematicians of the 20th century.
His work on what is now called the Ramanujan tau function, which evoked only a moderate response at that time, later proved to be profound and central to what is called the Theory of Modular Forms . Hecke, a great German mathematician who was one of the architects of the theory was born in the same year -1887-as Ramanujan: it does seem a great pity that the two never met. A conjecture of Ramanujan on the tau function was settled in 1974 by Pierre Deligne, a leading mathematician of our era. (boxed matter)
His work on what is now called the Ramanujan tau function, which evoked only a moderate response at that time, later proved to be profound and central to what is called the Theory of Modular Forms . Hecke, a great German mathematician who was one of the architects of the theory was born in the same year -1887-as Ramanujan: it does seem a great pity that the two never met. A conjecture of Ramanujan on the tau function was settled in 1974 by Pierre Deligne, a leading mathematician of our era. (boxed matter)One of the most fruitful techniques applied successfully to diverse problems in Number Theory is known as the Circle Method. This originates from the joint work Ramanujan did with Hardy on what is known as the partition function.
Ramanujan's Notebooks are a treasure house of beautiful formula and identities , set down without details. Providing proper proofs to these has been a challenge and at the same time, a public service to the mathematical community.Experience indicates that there is likely to be much more to many of these results than the formal beauty which by itself makes them attractive . It has been said that in the matter of formal manipulations Ramanujan has no equals in the history of mathematics, other than Euler and Jacobi.
Hardy is much less of an enigma even to us in India, than Ramanujan himself. He was, of course one of the major mathematical figures of the twentieth century and , as the Ramanujan story shows , he was a wonderful human being. He was also exceptionally articulate and a gifted writer of English prose. His little book, A mathematician's Apology-giving his view of his profession, makes delightful reading. Hardy was very much the ivory-tower intellectual and the book is not so much an 'apology' as an emphatic affirmation of his belief in the irrelevance of social relevance in the pursuit of pure science. He has also written an account of the Bertrand Russel affair-the turmoil in Cambridge caused by Russell"s unorthodox views and conduct during the war years 1914-18.
Hardy was an ardent cricket fan; so ardent indeed that he calibrated excellence in any field by cricketing greats: the highest accolade was to be in the 'Bradman class'! Interesting people were people who had 'spin' in them.
Hardy was an outstanding analysts as well as a member theorist: his work in analysis has in some ways been more influential than that in number theory. He was the leading expert on Infinite Series: his book Divergent Series was a classic of that period. He disapproved of theway mathematics was taught in Britain in his days and sought to reform the same. His book Pure Mathematics was an attempt in that direction. It was the first analysis book in English written in the European spirit, and proved a great success.
A not-so-well-known contemporary of Ramanunjan was K.Ananda Rau, a foundation member of Indian Academy of Sciences, Bangalore. His career had an altogether different kind of trajectory from Ramnujan's . He was born in Madras in 1893, (six years after Ramanujan ) into relative opulence and after a brilliant academic career of the normal kind through school and college in Madras, went to Cambridge in1914 and became a student of Hardy's . As a student he won the much coveted Smith Prize. He returned to Madras after completing his studies in 1919 and was immediately apointed as Professor of Mathematics at Presidency College, Madras. Anand Rau was an outstanding analyst who worked a great deal on summability, an area in which Hardy was a leading figure. A theorem named after Anand Rao figures in Hardy's book Divergent Series. He was from all accounts an inspiring teacher, held in great respect and affection by his students.Many of whom went on to become fine mathematicians themselves:some among them were leaders on the Indian scene and I will be speaking about them. Anand Rau retired from service in 1948 at the then mandatory age of 55, but remained mathematically active for more than a decade after that. He died in 1966.
A not-so-well-known contemporary of Ramanunjan was K.Ananda Rau, a foundation member of Indian Academy of Sciences, Bangalore. His career had an altogether different kind of trajectory from Ramnujan's . He was born in Madras in 1893, (six years after Ramanujan ) into relative opulence and after a brilliant academic career of the normal kind through school and college in Madras, went to Cambridge in1914 and became a student of Hardy's . As a student he won the much coveted Smith Prize. He returned to Madras after completing his studies in 1919 and was immediately apointed as Professor of Mathematics at Presidency College, Madras. Anand Rau was an outstanding analyst who worked a great deal on summability, an area in which Hardy was a leading figure. A theorem named after Anand Rao figures in Hardy's book Divergent Series. He was from all accounts an inspiring teacher, held in great respect and affection by his students.Many of whom went on to become fine mathematicians themselves:some among them were leaders on the Indian scene and I will be speaking about them. Anand Rau retired from service in 1948 at the then mandatory age of 55, but remained mathematically active for more than a decade after that. He died in 1966.
