Kalyanapuram Rangachari Parthasarathy (25 June 1936 – 14 June 2023) was an Indian statistician who was professor emeritus at the

Indian Statistical Institute The Indian Statistical Institute (ISI) is a public research university headquartered in Kolkata, India with centers in New Delhi, Bengaluru, Chennai and Tezpur. It was declared an Institute of National Importance by the Government of India und ...

and a pioneer of

quantum stochastic calculus Quantum stochastic calculus is a generalization of stochastic calculus to Commutative property, noncommuting variables. The tools provided by quantum stochastic calculus are of great use for modeling the random evolution of systems undergoing Measur ...

. Parthasarathy was the recipient of the

Shanti Swarup Bhatnagar Prize Shanti or Shanthi may refer to: In Sanskrit * Inner peace, a state of being mentally and spiritually at peace, with enough knowledge and understanding to keep oneself strong in the face of discord or stress * Kshanti, one of the paramitas of B ...

for Science and Technology in Mathematical Science in 1977 and the

TWAS Prize This is a list of recipients of the TWAS Prize, awarded annually by The World Academy of Sciences (TWAS) since 1985. Summary Agricultural Sciences Biology Chemistry Earth Sciences Engineering Sciences Mathematics ...

in 1996.

Biography

Parthasarathy was born on 25 June 1936 in

Madras Chennai, also known as Madras ( its official name until 1996), is the capital and largest city of Tamil Nadu, the southernmost state of India. It is located on the Coromandel Coast of the Bay of Bengal. According to the 2011 Indian ce ...

, into a modest but deeply religious

Hindu Hindus (; ; also known as Sanātanīs) are people who religiously adhere to Hinduism, also known by its endonym Sanātana Dharma. Jeffery D. Long (2007), A Vision for Hinduism, IB Tauris, , pp. 35–37 Historically, the term has also be ...

Brahmin Brahmin (; ) is a ''Varna (Hinduism), varna'' (theoretical social classes) within Hindu society. The other three varnas are the ''Kshatriya'' (rulers and warriors), ''Vaishya'' (traders, merchants, and farmers), and ''Shudra'' (labourers). Th ...

family. He completed his early years of schooling in

Thanjavur Thanjavur (), also known as Thanjai, previously known as Tanjore, Pletcher 2010, p. 195 is a city in the Indian state of Tamil Nadu. It is the 12th biggest city in Tamil Nadu. Thanjavur is an important center of southern Indian religion, art ...

, before moving back to Madras to complete his schooling from P. S. School in the

Mylapore Mylapore (also spelt Mayilapur), or Thirumayilai, is a neighbourhood in the central part of the city of Chennai, India. It is one of the oldest residential parts of the city. The locality is claimed to be the birthplace of the celebrated Tamil ...

neighbourhood of the city. He went on to study at the

Ramakrishna Mission Vivekananda College Ramakrishna Mission Vivekananda College, named after Swami Vivekananda, was formally inaugurated on 21 June 1946 by professor, philosopher, and politician, Sarvepalli Radhakrishnan. It is in Mylapore, the centre of Chennai, India, on 20 acres (81 ...

, where he completed the B.A. (Honours) course in

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. Parthasarathy then moved to

Kolkata Kolkata, also known as Calcutta ( its official name until 2001), is the capital and largest city of the Indian state of West Bengal. It lies on the eastern bank of the Hooghly River, west of the border with Bangladesh. It is the primary ...

to attend the Research and Training school at the

, where he completed his Ph.D., under the supervision of C. R. Rao in 1962. He was one of the "famous four" at ISI from 1956 to 1963, alongside R. Ranga Rao, Veeravalli S. Varadarajan, and S. R. Srinivasa Varadhan. He was awarded the first Ph.D. degree of ISI. He received the

for Science and Technology in Mathematical Science in 1977 and The World Academy of Sciences (TWAS) Prize for Mathematics in 1996. Parthasarathy was married to Shyama Parthasarathy. The couple had two sons. Parthasarathy died in

Delhi Delhi, officially the National Capital Territory (NCT) of Delhi, is a city and a union territory of India containing New Delhi, the capital of India. Straddling the Yamuna river, but spread chiefly to the west, or beyond its Bank (geography ...

on 14 June 2023, at the age of 86.

Research

Parthasarathy started his work on theoretical probability during his time at the

. He later worked at the

Steklov Mathematical Institute Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Ste ...

USSR Academy of Sciences The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (u ...

(1962–63), as lecturer where he collaborated with

Andrey Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet ...

. During this time, he continued to focus on the foundations of

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

. Later he came to the United Kingdom as a Professor of Statistics at

University of Sheffield The University of Sheffield (informally Sheffield University or TUOS) is a public university, public research university in Sheffield, South Yorkshire, England. Its history traces back to the foundation of Sheffield Medical School in 1828, Fir ...

(1964–68),

University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The University of Manchester is c ...

(1968–70) and later at

University of Nottingham The University of Nottingham is a public research university in Nottingham, England. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. Nottingham's main campus (University Park Campus, Nottingh ...

where he collaborated with Robin Lyth Hudson on their pioneering work in quantum stochastic calculus. After returning to India, he spent a few years at

Bombay University University of Mumbai is a public state university in Mumbai. It is one of the largest university systems in the world with over 549,000 students on its campuses and affiliated colleges. , the university had 711 affiliated colleges. It was est ...

and the

Indian Institute of Technology, Delhi Indian Institute of Technology Delhi (IIT- Delhi) is a public institute of technology located in Delhi, India. It is one of the 23 Indian Institutes of Technology created to be a Centre of Excellence for India's training, research and developme ...

, before returning to the new Indian Statistical Institute, Delhi Centre, in 1976, where he spent the next 20 years before retiring in 1996. He continued to remain as a

professor emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retirement, retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". ...

at the institute until the early 2020s. Parthasarathy is the namesake of Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants along with

Bertram Kostant Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician who worked in representation theory, differential geometry, and mathematical physics. Early life and education Kostant grew up in New York City, where he gradua ...

, R. Ranga Rao and Veeravalli S. Varadarajan which they introduced in 1967.K. R. Parthasarathy, R. Ranga Rao, and Veeravalli S. Varadarajan. "Representations of complex semi-simple Lie groups and Lie algebras". ''The Annals of Mathematics'' 85.3 (1967): 383–429 He collaborated with Ranga Rao and Varadarajan to write a paper on

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

lie groups In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Euclidean space, whereas ...

referred to as the PRV paper that was the foundation for further research on this topic. In addition to pioneering contributions to

, some of Parthasarathy's research areas included

quantum probability The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a ...

, foundations of

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...

stochastic processes In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stoc ...

, and group representations. He also served on many governmental committees.

Published works

Books

* K. R. Parthasarathy.

Probability measure In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies Measure (mathematics), measure properties such as ''countable additivity''. The difference between a probability measure an ...

s on

metric spaces In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are a general setting for ...

. Vol. 352.

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, 1967. * * * *

Papers

* * * * * * * * * * * * Parthasarathy, K. R., Ranga Rao, R., & Varadhan, S. R. S. (1962)
On the category of indecomposable distributions on topological groups. Transactions of the American Mathematical Society
102(2), 200-217.

References

External links

*

*https://web.archive.org/web/20120728070024/http://www.mathunion.org/Publications/Bulletins/39/parthasarathy.ps {{DEFAULTSORT:Parthasarathy, K. R. 1936 births 2023 deaths Indian statisticians 20th-century Indian mathematicians 21st-century Indian mathematicians Probability theorists Indian Statistical Institute alumni Academic staff of the Indian Statistical Institute Academics of the University of Manchester Academics of the University of Nottingham Academics of the University of Sheffield Scientists from Chennai TWAS laureates Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science