This document provides biographical information on several notable Indian mathematicians: - Amiya Charan Banerjee was a mathematician and educator who made contributions to astrophysics and galactic dynamics as a professor at Allahabad University. - Dwijendra Kumar Ray-Chaudhuri helped solve Kirkman's schoolgirl problem and made advances in coding theory and combinatorics as a professor at Ohio State University. - Harish-Chandra did fundamental work in representation theory and harmonic analysis on semisimple Lie groups as a faculty member at Princeton University. - Jayant Narlikar developed conformal gravity theory with Sir Fred Hoyle and advocated for steady state cosmology from his

1. Indian
Modern
Mathematicians

2. Amiya Charan Banerjee
 Amiya Charan Banerjee (23 January 1891 – 31 May 1968) was a mathematician and educator
popularly known as A.C.Banerjee or simply as Professor Banerjee
 . Family background
 His father Gyan Chandra Banerjee was a meritorious student of Presidency College and was a
class mate of Narendranath Dutta (later Swami Vivekananda) when they studied law. He
belonged to the zemindar family of Maheshtala in 24 Parganas district, now in West Bengal.
While a student he was attracted to the Brahmo Samaj, after listening to some of the speeches of
Keshub Chunder Sen. When he converted to Brahmo Samaj, his father tried to get him back to
the house by force but when he failed to do so, he disinherited him. He joined the judicial service
in Bihar and lived an independent life undeterred by what others thought and did. He married
Mrinalini, daughter of the Brahmo leader Nibaran Chandra Mukherjee.

3. Achievements
 On his return to the country, he spent some time in Patna but
as there was no suitable post vacant for him, he went to
Allahabad and started his teaching career as a professor.
Allahabad University was a great centre of learning, buzzing
with scientists such as Megh Nad Saha and Nil Ratan Dhar.
Prof. Banerjee made notable contributions in the field of astro-
physics and galactic dynamics. He was vice-chancellor of
Allahabad University from 1953-55. He was examiner for
doctoral thesis for several universities in India and abroad, and
went abroad a number of times on lecture tours. Government of
India had assigned to him a project for studying the
observatories in Europe and America and for recommending
improvements of Indian observatories. On retirement he helped
to develop Sri Chaitanya College at Habra in West Bengal. He
presided over the All India Brahmo Conference held in 1957

4.  Prof. Banerjee was nominated
president of the 56th session of the
Indian Science Congress to be held at
Mumbai in 1969 but he died
prematurely on 31 May 1968.
 He used to deliver lectures on
astronomy. He spoke on “Stellar
Evolution” at the Allahabad session of
the Indian Academy of Sciences in
1946.
 The road in front of his house in
Allahabad was named after him.

5. Dijen K. Ray-
Chaudhuri
 Dwijendra Kumar Ray-Chaudhuri (Born November 1,
1933) a Bengali-born mathematician and a statistician
is a professor emeritus at Ohio State University. He
and his student R. M. Wilson together solved
Kirkman's schoolgirl problem in 1968.
 He is best known for his work in design theory and the
theory of error-correcting codes, in which the class of
BCH codes is partly named after him and his Ph.D.
advisor Bose. Ray-Chaudhuri is the recipient of the
Euler Medal by the Institute of Combinatorics and its
Applications for his career contributions to
combinatorics. In 2000, a festschrift appeared on the
occasion of his 65th birthday.
 Ray-Chaudhuri was born in Narayanganj village in
Bengal, British India. He received his M.Sc. (1956) in
mathematics from the University of Calcutta and Ph.D.
in combinatorics (1959) from University of North
Carolina at Chapel Hill. He is married to Joyasree
Ray-Chaudhuri. They have three children.


6. Harish-Chandra
 Harish-Chandra (Harish Chandra Mehrotra; 11 October 1923 –
16 October 1983) was an Indian mathematician, who did
fundamental work in representation theory, especially
Harmonic analysis on semisimple Lie groups.
 LIFE
 Harish-Chandra was born in Kanpur (then Cawnpore), British
India. He was educated at B.N.S.D. College, Kanpur, and at the
University of Allahabad. After receiving his masters degree in
Physics in 1943, he moved to the Indian Institute of Science,
Bangalore for further studies in theoretical physics and worked
with Homi J. Bhabha.
 In 1945, he moved to University of Cambridge, Cambridge and
worked as a research student under Paul Dirac. While at
Cambridge, he attended lectures by Wolfgang Pauli, and during
one of them pointed out a mistake in Paul's work. The two were
to become life long friends. During this time he became
increasingly interested in mathematics. At Cambridge he
obtained his PhD in 1947.

7.  When Dirac visited Institute of Advanced Study,
Princeton, U.S.A. in 1947/48 he brought Harish-
Chandra as his assistant. It was at this stage that
Harish-Chandra decided to change over from physics to
mathematics.
 He was a faculty member at the Institute for Advanced
Study, Princeton, New Jersey from 1963.
 From 1968, until his death in 1983, he was IBM von
Neumann Professor in the School of Mathematics at the
Institute for Advanced Study, Princeton, New Jersey.
 He died of a heart attack while on an evening walk on
October 16, 1983, during a conference in Princeton in
honour of Armand Borel's 60th birthday. A similar
conference for his 60th birthday, scheduled for the
following year, instead became a memorial conference.
He is survived by his wife, Lalitha (Lily), and his
daughters Premala (Premi), and Devaki.

8. Work in mathematics
 He was influenced by the mathematicians Hermann
Weyl and Claude Chevalley. From 1950 to 1963 he was
at the Columbia University and worked on
representations of semisimple Lie groups. During this
period he established as his special area the study of
the discrete series representations of semisimple Lie
groups, which are analogues of the Peter–Weyl theory
in the non-compact case.
 He is also known for work with Armand Borel on the
theory of arithmetic groups; and for papers on finite
group analogues. He enunciated a philosophy of cusp
forms, a precursor of the Langlands philosophy.

9. Honors and awards
 He was a member of the National Academy of Sciences of the U.S.
and a Fellow of the Royal Society. He was the recipient of the Cole
Prize of the American Mathematical Society, in 1954. The Indian
National Science Academy honoured him with the Srinivasa
Ramanujan Medal in 1974.
 The mathematics department of B.N.S.D. College, Kanpur celebrates
his birthday every year in different forms, which includes lectures
from students and professors from various colleges, institutes and
students' visit to Harish-Chandra Research Institute.
 The Indian Government named the Harish-Chandra Research
Institute, an institute dedicated to Theoretical Physics and
Mathematics, after him.
 Robert Langlands wrote in a biographical article of Harish-Chandra:
 “
 He was considered for the Fields Medal in 1958, but a forceful
member of the selection committee in whose eyes Thom was a
Bourbakist was determined not to have two. So Harish-Chandra,
whom he also placed on the Bourbaki camp, was set aside.

10. Jayant Narlikar
 Dr. Jayant Vishnu Narlikar (born July 19,
1938) (Marathi: जयंत विष्णू नारळीकर) is an
Indian cosmologist.
 Narlikar is a proponent of the steady state
cosmology. He developed with Sir Fred
Hoyle the conformal gravity theory,
commonly known as Hoyle–Narlikar
theory. It synthesizes Albert Einstein’s
Theory of Relativity and Mach's Principle.
It proposes that the inertial mass of a
particle is a function of the masses of all
other particles, multiplied by a coupling
constant, which is a function of cosmic
epoch. In cosmologies based on this
theory, the gravitational constant G
decreases strongly with time.

11. Early life
 Narlikar was born in Kolhapur, India on July
19, 1938. His father, Vishnu Vasudev
Narlikar, was a mathematician who served as
a professor and later as the Head of the
Department of Mathematics at Banaras
Hindu University, Varanasi. Jayant's mother,
Sumati Narlikar, was a scholar of Sanskrit
language. He studied in Kendriya Vidyalaya
Banaras(till class 12) and Banaras Hindu
University(12th Onwards) campus, Varanasi.

12. Honours

 In year 2011 Hon.Narlikar received highest civilian award in
Maharashtra state which in MAHARASHTRA BHUSHAN.
Narlikar has received several national and international awards
and honorary doctorates. India’s second highest civilian honor,
Padma Vibhushan, was awarded to him in 2004 for his research
work. Prior to this, in 1965, he was conferred PADMA Bhushan.
 He received Maharashtra Bhushan Award for the year 2010.
 He is a recipient of Bhatnagar Award, M.P. Birla Award, and the
Prix Jules Janssen of the French Astronomical Society. He is an
Associate of the Royal Astronomical Society of London, and a
Fellow of the three Indian National Science Academies and the
Third World Academy of Sciences.
 Apart from his scientific research, Narlikar has been well known
as a communicator of science through his books, articles, and
radio & television programs. For these efforts, he was honored in
1996 by the UNESCO with the Kalinga Award.
 He was once featured on Carl Sagan's TV show Cosmos: A
Personal Voyage in the late 1980s. He received the Indira Gandhi
Award of the Indian National Science Academy in 1990.

13. Prasanta Chandra
Mahalanobis
 Prasanta Chandra Mahalanobis
FRS (Bengali: প্রশান্ত চন্দ্র মহলানবিস )
(29 June 1893 – 28 June 1972)
was an Indian scientist and
applied statistician. He is best
remembered for the Mahalanobis
distance, a statistical measure.
He made pioneering studies in
anthropometry in India. He
founded the Indian Statistical
Institute, and contributed to the
design of large scale sample
surveys.[1][2]

14. Honours
 Weldon Medal from Oxford University (1944)
 Fellow of the Royal Society, London (1945)
 President of Indian Science Congress (1950)
 Fellow of the Econometric Society, U.S.A. (1951)
 Fellow of the Pakistan Statistical Association (1952)
 Honorary Fellow of the Royal Statistical Society, U.K. (1954)
 Sir Deviprasad Sarvadhikari Gold Medal (1957)
 Foreign member of the Academy of Sciences of the USSR (1958)
 Honorary Fellow of King's College, Cambridge (1959)
 Fellow of the American Statistical Association (1961)
 Durgaprasad Khaitan Gold Medal (1961)
 Padma Vibhushan (1968)
 Srinivasa Ramanujam Gold Medal (1968)
 The government of India decided in 2006 to celebrate his birthday, 29 June,
as National Statistical Day.

15. Subrahmanyan
Chandrasekhar
 Subrahmanyan Chandrasekhar (October 19,
1910 – August 21, 1995)[1] was a British
India born Indian-American astrophysicist
who, with William A. Fowler, won the 1983
Nobel Prize for Physics for key discoveries
that led to the currently accepted theory on
the later evolutionary stages of massive
stars.[2][3] Chandrasekhar was the nephew of
Sir Chandrasekhara Venkata Raman, who
won the Nobel Prize for Physics in 1930.
 Chandrasekhar served on the University of
Chicago faculty from 1937 until his death in
1995 at the age of 84. He became a
naturalized citizen of the United States in
1953.

16. Awards
 Fellow of the Royal Society (1944)
 Henry Norris Russell Lectureship (1949)[9]
 Bruce Medal (1952)[10]
 Gold Medal of the Royal Astronomical Society (1953)[11]
 Rumford Prize of the American Academy of Arts and Sciences
(1957)[12]
 National Medal of Science, USA (1966)[13]
 Padma Vibhushan (1968)
 Henry Draper Medal of the National Academy of Sciences
(1971)[14]
 Nobel Prize in Physics (1983)
 Copley Medal of the Royal Society (1984)
 Honorary Fellow of the International Academy of Science
(1988)

17. Nobel prize
 He was awarded the Nobel Prize in
Physics in 1983 for his studies on the
physical processes important to the
structure and evolution of stars.
Chandrasekhar accepted this honor,
but was upset that the citation
mentioned only his earliest work,
seeing it as a denigration of a lifetime's
achievement. He shared it with
William A. Fowler.

18. Legacy
 Chandrasekhar's most notable work was the astrophysical
Chandrasekhar limit. The limit describes the maximum mass
of a white dwarf star, ~1.44 solar masses, or equivalently, the
minimum mass above which a star will ultimately collapse into
a neutron star or black hole (following a supernova). The limit
was first calculated by Chandrasekhar in 1930 during his
maiden voyage from India to Cambridge, England for his
graduate studies. In 1999, NASA named the third of its four
"Great Observatories" after Chandrasekhar. This followed a
naming contest which attracted 6,000 entries from fifty states
and sixty-one countries. The Chandra X-ray Observatory was
launched and deployed by Space Shuttle Columbia on July 23,
1999. The Chandrasekhar number, an important dimensionless
number of magnetohydrodynamics, is named after him. The
asteroid 1958 Chandra is also named after Chandrasekhar.
American astronomer Carl Sagan, who studied Mathematics
under Chandrasekhar, at the University of Chicago, praised
him in the book The Demon-Haunted World: "I discovered what
true mathematical elegance is from Subrahmanyan
Chandrasekhar."