Kalyanapuram Rangachari Parthasarathy, known to generations of mathematicians and probabilists simply as KRP, passed away on June 14 in New Delhi; he was 86. Professor Parthasarathy made numerous extremely deep contributions over a stunningly wide spectrum of mathematics: probability, quantum probability, graph theory, linear algebra, statistics and other mathematical domains. With his passing, India has lost an icon of 20th century mathematics.

Professor Parthasarathy was born in Madras, now Chennai, in 1936. After his BA (Honours) degree in Mathematics from Vivekananda College, he moved to the ISI (Indian Statistical Institute) in Calcutta in 1956, where he had C.R. Rao, D. Basu, Raghu Raj Bahadur and Radha Govind Laha, among others, as his teachers, and Ranga Rao, V.S. Varadarajan and Raghu Varadhan as his compatriots. Mostly by their personal interactions and incredible enterprise, the so-called “famous four ” learned a tremendous amount on ergodic theory, limit theorems on general (infinite-dimensional) Hilbert spaces and topological groups by using non-Fourier methods, Lie algebras, and information theory framed in the language of quantum mechanics. These were all extremely difficult topics, especially at that time, to master on one’s own. This deep and broad education during his ISI years was a catalyst for his ultimate profound and scholarly career in mathematics and quantum probability.

C.R. Rao and Mahalanobis persuaded Kolmogorov to give the convocation speech at the ISI while KRP was a student there. Kolmogorov agreed, but he refused to fly. Amazingly, it was possible to work out a trip from Moscow to Calcutta, and back, by boats and trains. Having met Kolmogorov at the ISI, Parthasarathy went to the Steklov Institute, where he attended seminar series by Kolmogorov, Dynkin, Gelfand and others. These had a huge influence on KRP’s subsequent work. Parthasarathy got his PhD from ISI Calcutta in 1962, supervised by C.R. Rao.

While at the ISI, he married his wife Shyama. The famous botanist T.A. Davis was working with J.B.S. Haldane, who was faculty at the ISI then, and very graciously, Davis found a modest campus accommodation for Professor Parthasarathy and his wife. Soon though, they left for Sheffield at Dr. Varadarajan’s suggestion. It was here that Eugene Lukacs happened to see KRP’s handwritten notes on probability measures and weak convergence in (mostly, separable) metric spaces; Academic Press published Parthasarathy’s classic Probability Measures on Metric Spaces in 1967. Nearly sixty years after its publication, it is still regarded as one of the main foundations for construction of the elegant one-dimensional empirical process theory, which has become a grand unifier of almost all of asymptotic theory. It has received 4,400 citations so far. Parthasarathy authored many other books and monographs on quantum probability and SDEs on abstract spaces, and these too are regarded as first-rate contributions. Special mentions may be made of the 1984 paper with Robin Hudson on quantum Itô formulas, which has received 1,600 citations; the 1963 article with Ranga Rao and Raghu Varadhan on probabilities on locally compact Abelian groups; the 1967 article with Ranga Rao and Varadarajan on representations of Lie groups; the 2000 paper with Rajendra Bhatia on positive definite functions; and the 1992 book on quantum stochastic calculus, which has received 1,700 citations. On the derivation of the Lévy–Khintchine formula for the characteristic function of an infinitely divisible distribution on the real line, Parthasarathy said that he read a comment made by Joe Doob that the proof rests entirely on positive definite functions, and there is no probability there. Parthasarathy said that this gave him the idea of considering positive definite kernels and that is how the monograph with K. Schmidt started. There are also numerous papers with Kalyan Sinha on operator theory and quantum diffusions, martingales and Markov processes; and many charming special papers, on graph theory, infinite divisibility, extreme points of convex sets, tomography, transmission rate of information, C* algebras, and several other interesting topics.

Following his years at Sheffield, he moved to Manchester and served as faculty of statistics for several years there. Parthasarathy and his family returned to India at the initiative of S.S. Shrikhande around 1967. He joined the CASM at Bombay (now Mumbai). C.R. Rao had already moved to Delhi from Calcutta (Kolkata), and some time around 1973, C.R. Rao suggested to Parthasarathy that he move to Delhi, as Rao very much wished that Parthasarathy join the Delhi center of the ISI, which was due to be opened soon. Parthasarathy accepted C.R. Rao’s suggestion and joined the IIT Delhi. One year later, in 1974, Indira Gandhi inaugurated the Delhi center of the ISI, where Parthasarathy was Distinguished Professor until his retirement in 1996. Among his many distinguished students are K. Balasubramanian, B.V.R. Bhat, Rajendra Bhatia and Inder Rana. He was Distinguished Professor Emeritus at ISI Delhi at the time of his passing.

For his contributions to the advancement of mathematical sciences, Professor Parthasarathy was given the Shanti Swarup Bhatnagar Prize in 1977.

Parthasarathy suggested that fresh PhDs should all start a seminar series, even if it is for just two or three people. They should talk to each other, generate ideas and spread these ideas by always writing notes on the seminar topics. That was his model for spreading world-class mathematics in India on a large scale. Parthasarathy had very original ideas about the role of mathematics in life. He said that sciences such as physics, chemistry and biology deal with external reality, like three dimensions. But there is also an internal reality, which is what mathematics treats, like n dimensions. And this internal reality then feeds into the external reality.

Parthasarathy was dedicated to the passionate pursuit of mathematics and probability all his life; he did not have other ambitions. But he did have other interests. He loved classic English literature and Indian classical music. He had a great sense of humor. He was a true and unfeigned academician, an esteemed representative of the best and golden days of the ISI, the days that still live in India’s romantic nostalgia.

He is survived by his wife Shyama and their two sons.

Written by Anirban DasGupta, Purdue University

Sources: Wikipedia, Conversation with B.V.R. Bhat, YouTube, Google Scholar, LinkedIn, Veethi.com