September 24, 2020

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*An account of the life and times of C.P. Ramanujam, one of the most outstanding mathematicians India was blessed to have. Find out all about his contributions that led to him leaving behind an ever-lasting legacy in mathematics.*

**Introduction**

People across the world know many great mathematicians of India, and Chidambaram Padmanabhan Ramanujam, popularly known as C.P. Ramanujam, is one such noted scholar. C.P. Ramanujam is often confused with well-known mathematician Srinivasa Ramanujan, famous for discovering that 1729 is the magic number in mathematics. Known for his works in the fields of algebraic geometry and number theory, there was more to C.P. Ramanujam than met the eye.

**Early life**

Ramanujam was born on 9th January 1938 in Chennai (then Madras) to a Tamil family and was the eldest of the seven siblings. His father, Chakravarthi Srinivasa Padmanabhan, was a Madras High Court advocate.

Ramanujam completed his higher secondary certification and graduation from the prestigious Loyola College in Chennai. His love for mathematics started at a young age, which was evident from his decision to specialise in the subject during his bachelor’s (honours) degree.

On the recommendation of Father Charles Racine, his friend and teacher, Ramanujam decided to pursue his love for mathematics by applying for admission to the School of Mathematics at the Tata Institute of Fundamental Research (TIFR) in Mumbai (then Bombay).

**Time at TIFR**

Before joining TIFR in 1957, Ramanujam spent some time with the Ramanujan Institute of Mathematics former director, and gained a deep understanding of analytic number theory. Speaking about Ramanujam’s brilliant grasping ability and knowledge of mathematics, K.G. Ramanathan, Ramanujam’s doctoral advisor at TIFR, wrote in a tribute to Ramanujam, “... he learned mathematics with avidity and speed that was often frightening.

He had given expert Colloquium talks and participated in seminars and displayed within two years of stay, versatility, and depth in mathematics which are rare (sic).”

It was common for renowned mathematicians from across the globe to give lectures at TIFR, and a tradition for graduate students to write lecture notes for the courses the mathematicians delivered.

As a first-year graduate student, Ramanujam wrote the notes for German mathematician Max Deuring’s lectures about the Theory of Algebraic Functions of One Variable.

Working on these lecture notes piqued Ramanujam’s interest in algebraic number theory. He went on to become an expert in not just algebraic geometry and analytic number theory but many other allied subjects too.

Ramanujam’s notes were appreciated, and he received praise for his work from several scholars, such as Russian mathematician I.R. Shafarevich and American mathematician David Bryant Mumford. Both these scholars spoke highly of how Ramanujam’s corrected many of their mistakes.

In the preface of his book Abelian Varieties, Mumford even mentioned that the work was a joint effort between him and Ramanujam, and Ramanujam helped improve the lectures.

Interestingly, while he was working with Mumford, Ramanujam started learning German, Italian, and French on his own to study mathematical works in their original form. There were quite a few non-English mathematical works in his library.

**Achievements**

In 1961, following the suggestion of K.G. Ramanathan, Ramanujam started working on a problem related to German number theorist Carl Ludwig Siegel’s work. Ramanujam’s simplification of Siegel’s method and his solution to Siegel’s problem in relation to Waring’s problem were brilliant.

In recognition of Ramanujam’s work on number theory, TIFR promoted him to the post of associate professor. Ramanujam protested strongly against this promotion, stating he was undeserving of the position. However, his friends and colleagues convinced him to accept the offer.

In 1971, he made a significant contribution to algebraic geometry by clarifying the Kodaira Vanishing Theorem. In 1973, he was elected the Fellow of the Indian Academy of Sciences. Moreover, a memorial hall at the University of Genoa’s former Istituto di Matematica (Institute of Mathematics) was named after Ramanujam after his demise.

**Publications**

- During his illustrious career, Ramanujam authored several publications. Some of his most noted works include:
- Cubic Forms Over Algebraic Number Fields published in Volume 59 of Proceedings of the Cambridge Philosophical Society (1963)
- Sums of m-th Powers in p-Adic Rings in Volume 10 of Mathematika (1963)
- A Note on Automorphism Groups of Algebraic Varieties published in Volume 156 of Mathematische Annalen (1964)
- On a Certain Purity Theorem published in Volume 34 of the Journal of the Indian Mathematical Society (1970)
- A Topological Characterisation of the Affine Plane as an Algebraic Variety published in Volume 94 of Annals of Mathematics (1971)
- Remarks on the Kodaira Vanishing Theorem published in Volume 36 of the Journal of the Indian Mathematical Society (1972)
- On a Geometric Interpretation of Multiplicity published in Volume 22 of Inventiones Mathematicae (1973), and
- Supplement to the Article “Remarks on the Kodaira Vanishing Theorem” published in Volume 38 of the Journal of the Indian Mathematical Society (1974).

**Struggle with schizophrenia and depression**

In 1964, Ramanujam was in Paris upon David Mumford and German mathematician Alexander Grothendieck’s invitation. It was then that he had an attack and was diagnosed with schizophrenia with severe depression.

His diagnosis made him feel inadequate for research in mathematics, so he decided to quit his position at TIFR. He was later offered the position of a tenured professor at the Panjab University, which he took up. However, he stayed there for only about 8 months because he had to visit Chennai for treatment of his illness.

Ramanujam then decided to rejoin his alma mater, TIFR. He was also invited to the Institut des Hautes Etudes Scientifiques, Paris, for six months. However, due to another bout of illness, he was forced to return to Chennai for treatment before his stay.

**Days leading up to his demise**

The recurrent illness forced Ramanujam to submit his resignation letter to TIFR. It was at this time that Ramanujam, upon receiving an invitation from Mumford, went on to become a visiting professor at the University of Warwick during the algebraic geometry year. Ramanujam also visited Italy for a while.

After returning to India, TIFR offered him a professorship in Bangalore, where the institute had just started a new programme dealing with applied mathematics. His students and colleagues loved and respected him dearly. During his time in Bangalore, he tried to take his life during several periods of illness. He also tried to move away from TIFR again.

On 27th October 1974, just before the Indian Institute for Advanced Studies at Simla could offer him a permanent professorship, C.P. Ramanujam took an overdose of barbiturates, leading to his demise and the loss of a great mathematician of India.

**Conclusion**

C.P. Ramanujam was a mathematical genius, and his contributions continue to be celebrated by scholars. His work, without a doubt, left an indelible mark on the world of mathematics if you want to know more or ask any questions about this brilliant mathematician, comment below!