C. P. Ramanujam

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C. P. Ramanujam
Born 9 Jan 1938
Madras, India
Died 27 Oct 1974
Bangalore, India
Citizenship India
Nationality Indian
Fields Mathematics
Institutions Tata Institute for Fundamental Research
Alma mater Tata Institute for Fundamental Research
Doctoral advisor K. G. Ramanathan
Notable awards Fellow, Indian Academy of Sciences

Chakravarthi Padmanabhan Ramanujam (January 9, 1938 – October 27, 1974) was an Indian mathematician who worked in the fields of Number theory and Algebraic geometry. He got elected Fellow of the Indian Academy of Sciences in 1973. Like Srinivasa Ramanujan, his namesake, Ramanujam also had a very short life.

As David Mumford put it, Ramanujam felt that the spirit of mathematics demanded of him not merely routine developments but the right theorem on any given topic. "He wanted mathematics to be beautiful and to be clear and simple. He was sometimes tormented by the difficulty of these high standards, but in retrospect, it is clear to us how often he succeeded in adding to our knowledge, results both new, beautiful and with a genuinely original stamp".

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[edit] Childhood

Ramanujam was born in Chennai, India, as the eldest of seven, to Chakravarthi Srinivasa Padmanabhan. He exhibited an intense curiosity at an early age. At the age of ten he was building large complex mechanical gadgets with his Lego set. At twelve he had a small chemistry lab in his room and was constantly tinkering with different chemicals,trying out different experiments. His curiosity and yen for learning was unquenchable. He was known to torment his school teachers and gained a reputation for embarrassing his teachers with difficult questions. He finished his schooling and joined Loyola College in Chennai in 1952. His specialization was to be mathematics and he set out to master it with vigour and passion. His teacher and friend at this time was Father Racine. Father Racine was a missionary who had obtained his doctorate under the supervision of Elie Cartan, one of the great mathematicians of the first half of the twentieth century. Father Racine quickly realised that he had a talented student on his hands. On Father Racine's encouragement and recommendation, Ramanujam applied to the graduate school at the Tata Institute of Fundamental Research in Bombay and was admitted to TIFR. His father had wanted him to join the Indian Statistical Institute in Kolkata as he had passed the entrance exam there meritoriously.

[edit] Early career

He set out for Mumbai at the age of eighteen to pursue his interest in mathematics. He and his friend and schoolmate Raghavan Narasimhan, and S. Ramanan joined TIFR together in 1957. At the Tata Institute there was a stream of first rate visiting mathematicians from all over the world. It was a tradition for some graduate student to write up the notes of each course of lectures. Accordingly, Ramanujam wrote up in his first year, the notes of Max Deuring's lectures on Algebraic functions of one variable. It was a nontrivial effort and the notes were written clearly and were well received. The analytical mind was much in evidence in this effort as he could simplify and extend the notes within a short time period. "He could reduce difficult solutions to be simple and elegant due to his deep knowledge of the subject matter" states Ramanan. "Max Deuring's lectures gave him a taste for Algebraic Number Theory. He studied not only algebraic geometry and analytical number theory of which he displayed a deep knowledge but he became an expert in several other allied subjects as well".

His Ph.D guide, K. G. Ramanathan[1] states that Ramanujam displayed within two years of his stay, versatility and depth in mathematics which was rare and somewhat frightening. However, there were no concrete results commensurate with his mathematical breadth and depth and this soon led to frustration. His wide foray into a variety of topics led to a dispersed knowledge but it did not have 'big cash value' states Ramanathan. Ramanujam was frustrated and felt that he was not worthy of staying on in the Institute. "He applied to different universities to teach mathematics and fortunately for him he was not accepted anywhere" states Ramanathan. On his guide's suggestion he began working on a problem relating to the work of the great German number theorist C. L. Siegel. His insight and knowledge finally bore fruit and he solved the long outstanding problem in a remarkably short time. In the course of proving the main result[2] to the effect that every cubic form in 54 variables over any algebraic number field K had a non-trivial zero over that field, he had also simplified the earlier method of Siegel. Although he felt that with a little more effort, it could be reduced even to Davenport's 29, valid for the rational number field, Ramanujam was not interested in pursuing it. He wanted to move on and tackle more exciting problems. He took up Waring's problem in algebraic number fields and got interesting results. In recognition of his work and his contribution to Number Theory, the Institute promoted him as Associate Professor. He protested against this promotion as 'undeserved', and had to be persuaded to accept the position. He proceeded to write his thesis in 1966 and took his Doctoral examination in 1967. Dr. Siegel who was one of the examiners was highly impressed with the young man's depth of knowledge and his great mathematical abilities.

Ramanujam was a scribe for Shafarevich's course of lectures in 1965 on minimal models and birational transformation of two dimensional schemes. Professor Shafarevich[3] subsequently wrote to say that Ramanujam not only corrected his mistakes but complemented the proofs of many results. The same was the case with Mumford's lectures on abelian varieties which was delivered at TIFR around 1967. Mumford wrote in the preface to his book that the notes improved upon his work and that his current work on abelian varieties was a joint effort between him and Ramanujam. A little known fact is that during this time he started teaching himself German, Italian, Russian and French so that he could study mathematical works in their original form. His personal library contained quite a few non-English mathematical works.

[edit] Personality and other interests

He could quickly enthuse others with his passion for maths and freely gave of his time and knowledge to whoever sought him out. He did not just speak the language of mathematics. His finer sensibilities led him to appreciate fine pieces of literary work, both fiction and non-fiction.He always loved reading and gifting books to others. He had a fine ear for music and it was his second passion after mathematics. His favorite musician was Dr. M. D. Ramanathan, a maverick concert musician who was not very popular because of his classicalism. Ramanujam would invariably attend his concerts when he was in Chennai. During his early thirties he wanted to learn music and bought himself a flute and learnt to play it.He sought out people with whom he could discuss music and loved their company. Like many a connoisseur of arts, he loved good food. In his early years he took to smoking and later discovered the joy of smoking a pipe. His other hobbies were chess, tennis, carrom and Go. He would however resume his mathematical scribblings on any scrap of paper that was available whenever an idea came to him. His mathematical mind was effortlessly clicking away even when he was relaxing and enjoying himself. Ramanujam was extremely large hearted and generous to a fault and was known time and again to empty out his wallet to anyone in the street who approached him.

[edit] Illness and death

Between 1964 and 1968, he was making great strides in Number theory and his contacts with Shafarevich and Mumford led him on to Algebraic Geometry. According to Ramanathan and other colleagues, his progress and deep understanding of Algebraic Geometry was phenomenal. Mumford highly commended his work in this area. Ramanujam gained such a deep understanding of his specialization, that he was sought after by his colleagues and was a source of inspiration to them. In 1964, based on his participation in the International Colloquim on Differential Analysis, he earned the respect of Grothendieck and Mumford who invited him to Paris and Harvard. He accepted the invitation and was in Paris, but for a brief period. Things would not be the same. He was burning the candle at both ends and it would take its toll. He was diagnosed in 1964 with schizophrenia with severe depression and left Paris for Chennai. He felt very strongly that he was not suited for mathematical research and decided to quit his position at TIFR. His resignation was however not accepted by the Institute.It will always be a mystery as to whether his unassuming, humble demeanour and modesty in some ways contributed to his illness. A true savant,imbued with a rare modesty and humility, he felt that what he had achieved did not deserve recognition.

He quit his post at Mumbai in 1965 after a bout of illness and secured a tenured position as a Professor in Chandigarh, Punjab. There he met the young student Chitikila Musili, who was from a very humble background. Though Musili knew little mathematics at that time, Ramanujam spent a lot of time with him, teaching him and encouraging him. He suggested to the Institute that he was a bright student and could be directly taken as a graduate student without the ritual of an interview. Musili was later to prove interesting results in the geometry connected with the theory of Lie groups and wrote good expository books. Ramanujam stayed in Chandigarh only 8 months and he had to return to Chennai again for treatment. TIFR was his real home and he was back there again in June 1965. Around this time he accepted an invitation from Insitut Des Hautes Etudes Scientifiques, near Paris. He was barely there before he was flown back to Chennai. Unfortunately schizophrenia, a highly treatable condition today, was not properly diagnosed and treated at that time. Thus he continued until the end of his life - to be highly creative for short periods before the recurrent illness overtook him. Again, in 1970, he sent his resignation letter to TIFR but the institute would not take it seriously. Around this time, Mumford invited him to Warwick as a visiting professor during the Algebraic Geometry year. Mumford writes that he spent many delightful evenings with him and that his presence contributed importantly to the success of the Algebraic Geometry year [2]. A famous paper written during this time, by Mike Artin and David Mumford acknowledges Ramanujam's suggestions and help.He also had a short tenure at Turin where he was widely appreciated and accepted. It is said that a commemorative hall has been named after him in Turin.

Back in India after his year at the University of Warwick, Ramanujam requested for a Professorship at the Tata Institute but to be made tenable in their Bangalore campus. The Tata Institute had an applied mathematics wing in Bangalore. Although Ramanjuam had nothing to do with this area, the Institute, wishing him to continue his research, made a special arrangement by which he could stay and work there. By this time he was deeply affected and depressed by his illness and wanted to try magical cures. He was put in charge of a new branch dealing with applied mathematics. He settled down in Bangalore but again in the depths of depression caused by his illness, he tried to leave the Institute and obtain a university teaching post. During one of the attacks, he tried to take his life, but was rescued in time. However, late one evening on October 27 1974, after a lively discussion with a visiting foreign professor he took his life with an overdose of barbiturates. He was barely thirty seven.

Ramanathan writes in [2] - In his meteoric career he had done brilliant work in Number Theory and Algebraic Geometry. In his death the country in general and the Tata Institue in particular,lost an outstanding mathematician, a warm colleague and a great human being.

S.Ramanan writes in [3] - For sheer elegance and economy, I have come across few mathematicians who were C P Ramanujam's equal. He made so many remarks which clarified and threw light on different branches of mathematics that personally I derived immense pleasure from his company. There is no question about his stature in mathematics.

[edit] Notes, papers and publications of C. P. Ramanujam

  • Cubic Forms over algebraic number fields: Proceedings of the Cambridge Philosophical Society, 59 (1963), 683-705
  • Sums of m-th powers in p-adic rings: Mathematika, 10 (1963), 137-146
  • A note on automorphism groups of algebraic varieties: Mathematische Annalen, 156 (1964), 25-33
  • On a certain purity theorem: Journal of the Indian Mathematical Society, 34 (1970), 1-10
  • A topological characterisation of the affine plane as an algebraic variety: Annals of Mathematics, 94 (1971), 69-88
  • Remarks on the Kodaira Vanishing Theorem: Journal of the Indian Mathematical Society, 36, (1972), 41-51
  • The invariance of Milnor's number implies the invariance of the topological type (jointly with Le Dung Trang): American Journal of Mathematics, 98 (1976),67-78
  • On a geometric interpretation of multiplicity: Inventiones Mathematicae, 22 (1973), 63-67
  • Supplement to the article, "Remarks on the Kodaira Vanishing Theorem": Journal of the Indian Mathematical Society, 38,(1974), 121-124
  • Appendix to the paper of C. S. Seshadri entitled Quotient space by an abelian variety: Mathematische Annalen, 152,(1963), 192-194
  • The theorem of Tate, Appendix I to the book entitled Abelian Varieties by D.Mumford: Tata Institute of Fundamental Research Studies in Mathematics, (1974), 240-260

[edit] Contributed papers

  • Le Dung Trang: The geometry of the monodromy
  • Masayoshi Nagata : on Euclid Algorithm
  • M. S. Raghunathan: Principal bundles on affine space
  • C. S. Seshadri: Geometry of G/P-I
  • M. V. Nori: Varieties with no smooth embeddings
  • D. Mumford: Some footnotes to the work of C. P. Ramanujam
  • S. Raghavan: Singular modular forms of degrees
  • M. Raynard: Contre-exemple au "vanishing theorem" en caracteristique p > 0
  • E. Bombieri and F. Catanese: The tricanonical map of a surface with K = 2,P = 0
  • M. S. Narasimhan and S. Ramanan: Geometry of Hecke cycles-I
  • B. Teissier: On a Minkowski-type inequality for multiplicities-II

[edit] References

  1. ^ 1
  2. ^ 2
  3. ^ 3
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