Another figure of importance in Indian mathematics of that time was Vaidyanathaswamy, also from Madras. He too went to England, not Cambridgethough, to work with some British mathematicians , but that was after some years as a research scholar at the University of Madras.
I should like to emphasize that in his case as well as in the case of Anand Rau, their career decisions were taken well before the Ramanujan story broke out. Also most of Vaidyanathaswamy's mathematical interests were far removed from those of Ramanujan's and he was among the earliest to venture into areas such as Symbolic Logic, Lattice Theory and Topology that were not British favourites of his times. After his return from England in 1925, he spent a year in Benares and joined Anand Rau in Madras. The two men joined forces to create a lively and congenial atmosphere for mathematics students in Madras. Madras University administration, in its infinite wisdom , kept him as a Reader till hisretirement in 1952. After retirement , he worked for a few years at the Indian Statistical Institute in Calcutta and later at Sri. Venkateswara University in Tirupathi.
Vaidyanathaswamy seems to have been cast in the mould of traditional Indian Scholarship. He was a keen student of Aurobindo's philosophy and studied Vedic texts in depth, offering his own interpretations.
Number theory , Ramanujan's area of interest , naturally has many adherents in the country; but work that had a truly great impact came only in the mid-thirties, and it came from S.S.Pillai. Pillai was born in 1901 in the Tirunelveli district of Tamil nadu. His mother died within a year of his birth and he was brought up by his father with the help of an aged woman relative. He made good progress at school, but tragedy struck again; his father passed away when he was in the final year of school.His talents had earned him the lasting affection of a teacher, Sastriar, who stepped in to help him continue his education.Pillai also secured scholarships and completed the B.A. degree at Maharaja's College at Trivandrum and moved to Madras where he became a student of Anand Rau for whom he cherished life long affection and respect. He soon proved himself to be a researcher of the first rank and after taking his Ph.D. at Madras took up his first job at Annamalai University; he later moved to Trivandrum then again to Calcutta and finally back to Madras University.
Number theory , Ramanujan's area of interest , naturally has many adherents in the country; but work that had a truly great impact came only in the mid-thirties, and it came from S.S.Pillai. Pillai was born in 1901 in the Tirunelveli district of Tamil nadu. His mother died within a year of his birth and he was brought up by his father with the help of an aged woman relative. He made good progress at school, but tragedy struck again; his father passed away when he was in the final year of school.His talents had earned him the lasting affection of a teacher, Sastriar, who stepped in to help him continue his education.Pillai also secured scholarships and completed the B.A. degree at Maharaja's College at Trivandrum and moved to Madras where he became a student of Anand Rau for whom he cherished life long affection and respect. He soon proved himself to be a researcher of the first rank and after taking his Ph.D. at Madras took up his first job at Annamalai University; he later moved to Trivandrum then again to Calcutta and finally back to Madras University.
It is in the thirties at Annamalai university that Pillai's talents were in full bloom and he cracked a problem that was engaging some of the finest minds. David Hilbert had shown that for every inter k>o, there is a smallest integer g(k)>o, such that every positive integer can be expressed as a sum of g(k)kth powers . Pillai's work centered on the exact determination of g(k)kth. He achieved the complete determination for k> 7, a superb achievement by any reckoning. He went on a little later to tackle the even more difficult case k=6. However a controversy over priorities involving the American mathematician L.E.Dickson was a cause for some distress to Pillai and his Indian colleagues.Pillai published his great papers in Indian Journals which did not have a wide circulation; nevertheless , recognition did come eventually for these outstanding contributions, but tragedy struck once more before he could savor his success. On 31st August 1950, Pillai died in an air crash over Egypt; he was on his way to the US , his first trip abroad to spend a year at the Institute for Advanced Study in Princeton, where he had been invited. The news was received with great shock by the many mathematicians assembled at Harvard, where Pillai was to participate in the International Congress of Mathematicians before going to Princeton. Pillai's work in the 'waring' problem-the determination of g(k) is a piece that has given him a permanent place in the history of mathematics.
The determination of g(k) for all k has now been completed, the case k=4 was the one that defined mathematicians the longest, till about 10 years ago when another Indian ,R.Balasubramian in collaboration with two Frenchman , Deshouillers and Dress settled the matter. Pillai had numerous other important contributions as well. There is little doubt that Pillai would have achieved a great deal more if his life had not been cut short so abruptly.
' Pillai ' in the words of Prof.K.Chandrasekharan ( of whom too I will speak ) ' was a person of genuine modesty and remarkable simplicity. He possessed that rare quality among intellectuals-intellectual honesty-which endeared him to his friends, but lost him many material advantages. ' ' He was ' says Chandrasekharan , ' unsophisticated in a peculiar sense.
In the early part of the twentieth century, British mathematics held sway over us. It did produce some beneficial results. But in the twenties and thirties, the most exciting developements in mathematics were taking place in Paris and Gottingen, not Cambridge. These developments seem to have had no serious immediate impact on the Indian scene. Summability, an area of great interest to Hardy was pursued by many Indians , including Ananda Rau and many of his students and they made very substantial contributions. But the subject continued to be pursued by many Indians long after it had ceased to offer exciting challenges. So there was an element of truth in the impish comment ' Hardy spoilt many Indian mathematicians : but of course Ramanujan was much too great to be spoilt. ' That brings me to the man who made that statement-Andre Weil.
Andre Weil was one of the greatest mathematicians of the 20th century. He was a colorful personality with with a powerful sense of humour and was not averse to using it to cause discomfort. He spent two years 1930 to 1932 in India as a Professor of Mathematics at Aligarh Muslim University. He tells the amusing story of how this came about in his auto biography. Syed Ros Masood then Education Minister to the Nizam of Hyderabad was vacationing in Europe when he was appointed Vice Chancellor of the Aligarh Muslim University, founded by his grandfather Syed Ahmed Khan. He decided to cut short his stay in Paris and return home , but he wanted to recruit a suitable person for a chair in French Culture at the university, before he left Europe . Towards this end he met with the famous French Indologist Slyvain Levy, who summoned Weil to their presence. Weil , who had just completed his doctorate in mathematics as a student at the famed Ecole Normale Superieure in Paris, was in touch with SlyvainLevy because of his interest in India; among other things, Weil had been keenly following a course of lectures on Kalidasa's Meghadutam given by Levy at the Sorbonne. The interview was brief; Masood offered the chair on the spot and Weil accepted it. But six months later, when the formal offer came, it was a chair in mathematics, not French Culture that was offered! Weil says that he never found out when exactly Masood came to know of his mathematical credentials!
Andre Weil was one of the greatest mathematicians of the 20th century. He was a colorful personality with with a powerful sense of humour and was not averse to using it to cause discomfort. He spent two years 1930 to 1932 in India as a Professor of Mathematics at Aligarh Muslim University. He tells the amusing story of how this came about in his auto biography. Syed Ros Masood then Education Minister to the Nizam of Hyderabad was vacationing in Europe when he was appointed Vice Chancellor of the Aligarh Muslim University, founded by his grandfather Syed Ahmed Khan. He decided to cut short his stay in Paris and return home , but he wanted to recruit a suitable person for a chair in French Culture at the university, before he left Europe . Towards this end he met with the famous French Indologist Slyvain Levy, who summoned Weil to their presence. Weil , who had just completed his doctorate in mathematics as a student at the famed Ecole Normale Superieure in Paris, was in touch with SlyvainLevy because of his interest in India; among other things, Weil had been keenly following a course of lectures on Kalidasa's Meghadutam given by Levy at the Sorbonne. The interview was brief; Masood offered the chair on the spot and Weil accepted it. But six months later, when the formal offer came, it was a chair in mathematics, not French Culture that was offered! Weil says that he never found out when exactly Masood came to know of his mathematical credentials!
Weil packed his bags and left for Aligarh to take up the headship of the Mathematics Deparment there, armed with powers to hire and fire faculty - he was all of 23!The contrast between the supreme confidence of the Normalien ( as students of the Ecole Normale Superieure are known ) and the diffidence of the clerk from the Port- Trust is striking. but it would hardly surprise the sociologist . Weil promptly sacked one of his three colleagues, removed another temporarily and let the third continue , only to regret that decision soon.Weil spent two years in Aligarh during which he made many friends, not all of whom were academics. He had a good measure of the generally poor quality of mathematics in the country, but was pleasantly surprised to come across some talented young people of promise. He recruited one of them, T.Vijayaraghavan, a student of Hardy, to the vacant post in the department; this despite the fact that Vijayaraghavan lacked formal qualifications. The two struck up a lasting friendship. Apart from their common interest in mathematics, Vijayaraghavan with his scholarship in Tamil and Sanskrit, could cater to Weil's interest in Indian culture. Weil also came to know other Indian Mathematicians like Kosambi Chowla. He seems to have travelled a good deal. That included a trip to Trivandrum to participate in an Annual Meeting of the Indian Mathematical Society. On his way to Trivandrum, in Chennai he made the acquaintance of Ananda Rau and Vydainathswamy. His experience in Trivandrum provide some amusement . Younger men at the meeting had to device ingenious ways of reconciling some of the older colleagues' insistence on observing caste taboos with the possible sensitivities of the mlecha present among them.
