Srinivasa Ramanujan Biography
Born: December 22, 1887
Died: April 26, 1920
Achievements: Ramanujan independently discovered results of Gauss,
Kummer and others on hypergeometric series. Ramanujan's own work on
partial sums and products of hypergeometric series have led to major
development in the topic. His most famous work was on the number p(n)
of partitions of an integer n into summands.
Srinivasa Ramanujan was a mathematician par excellence. He is widely believed
to be the greatest mathematician of the 20th Century. Srinivasa Ramanujan made
significant contribution to the analytical theory of numbers and worked on elliptic
functions, continued fractions, and infinite series.
Srinivasa Aiyangar Ramanujan was born on December 22, 1887 in Erode, Tamil
Nadu. His father worked in Kumbakonam as a clerk in a cloth merchant's shop.
At the of five Ramanujan went to primary school in Kumbakonam. In 1898 at age
10, he entered the Town High School in Kumbakonam. At the age of eleven he
was lent books on advanced trigonometry written by S. L. Loney by two lodgers
at his home who studied at the Government college. He mastered them by the age
of thirteen. Ramanujan was a bright student, winning academic prizes in high
At age of 16 his life took a decisive turn after he obtained a book titledquot; A
Synopsis of Elementary Results in Pure and Applied Mathematicsquot;. The book was
simply a compilation of thousands of mathematical results, most set down with
little or no indication of proof. The book generated Ramanujan's interest in
mathematics and he worked through the book's results and beyond. By 1904
Ramanujan had begun to undertake deep research. He investigated the series (1/n)
and calculated Euler's constant to 15 decimal places. He began to study the
Bernoulli numbers, although this was entirely his own independent discovery. He
was given a scholarship to the Government College in Kumbakonam which he
entered in 1904. But he neglected his other subjects at the cost of mathematics
and failed in college examination. He dropped out of the college.
Ramanujan lived off the charity of friends, filling notebooks with mathematical
discoveries and seeking patrons to support his work. In 1906 Ramanujan went to
Madras where he entered Pachaiyappa's College. His aim was to pass the First
Arts examination which would allow him to be admitted to the University of
Madras. Continuing his mathematical work Ramanujan studied continued
fractions and divergent series in 1908. At this stage he became seriously ill again
and underwent an operation in April 1909 after which he took him some
considerable time to recover.
I have had no university education but I have undergone the ordinary school
course. After leaving school I have been employing the spare time at my disposal
to work at mathematics. I have not trodden through the conventional regular
course which is followed in a university course, but I am striking out a new path
for myself. I have made a special investigation of divergent series in general and
the results I get are termed by the local mathematicians as 'startling'.
Valmiki The most fundamental contribution of ancient India in
mathematics is the invention of decimal system of enumeration, including the
invention of zero. The decimal system uses nine digits (1 to 9) and the symbol
zero (for nothing) to denote all natural numbers by assigning a place value to the
digits. The Arabs carried this system to Africa and Europe.
The Vedas and Valmiki Ramayana used this system, though the exact dates of
these works are not known. MohanjoDaro and Harappa excavations (which may
be around 3000 B.C. old) also give specimens of writing in India. Aryans came
1000 years later, around 2000 B.C. Being very religious people, they were deeply
interested in planetary positions to calculate auspicious times, and they
developed astronomy and mathematics towards this end. They identified various
nakshatras (constellations) and named the months after them. They could count
up to 1012, while the Greeks could count up to 104 and Romans up to 108. Values
of irrational numbers such as and were also known to them to a high
degree of approximation. Pythagoras Theorem can be also traced to the Aryan's
Sulbasutras. These Sutras, estimated to be between 800 B.C. and 500 B.C., cover
a large number of geometric principles. Jaina religious works (dating from 500
B.C. to 100 B.C.) show they knew how to solve quadratic equations (though
ancient Chinese and Babylonians also knew this prior to 2000 B.C.). Jainas used
as the value of (circumference = x Diameter). They were very fond of
large numbers, and they classified numbers as enumerable, unenumerable and
infinite. The Jainas also worked out formulae for permutations and combinations
though this knowledge may have existed in Vedic times. Sushruta Samhita
(famous medicinal work, around 6th century B.C.) mentions that 63
combinations can be made out of 6 different rasas (tastes -bitter, sour, sweet,
salty, astringent and hot).
In the year 1881 A.D., at a village named Bakhshali near Peshawar, a farmer
found a manuscript during excavation. About 70 leaves were found, and are now
famous as the Bakhshali Manuscript. Western scholars estimate its date as
about third or fourth century A.D. It is devoted mostly to arithmetic and algebra,
with a few problems on geometry and mensuration.
With this historical background, we come to the famous Indian
(1114 A.D. -1185 A.D.) or Bhaskaracharaya is
the most well known ancient Indian mathematician. He was born in 1114 A.D. at
Bijjada Bida (Bijapur, Karnataka) in the Sahyadari Hills. He was the first to
declare that any number divided by zero is infinity and that the sum of any
number and infinity is also infinity. He is famous for his book Siddhanta
Siromani (1150 A.D.). It is divided into four sections -Leelavati (a book on
arithmetic), Bijaganita (algebra), Goladhayaya (chapter on sphere -celestial
globe), and Grahaganita (mathematics of the planets). Leelavati contains many
interesting problems and was a very popular text book. Bhaskara introduced
chakrawal, or the cyclic method, to solve algebraic equations. Six centuries later,
European mathematicians like Galois, Euler and Lagrange rediscovered this
method and called it quot;inverse cyclicquot;. Bhaskara can also be called the founder of
differential calculus. He gave an example of what is now called quot;differential
coefficientquot; and the basic idea of what is now called quot;Rolle's theoremquot;.
Unfortunately, later Indian mathematicians did not take any notice of this. Five
centuries later, Newton and Leibniz developed this subject. As an astronomer,
Bhaskara is renowned for his concept of Tatkalikagati (instantaneous motion).
After this period, India was repeatedly raided by muslims and other rulers and
there was a lull in scientific research. Industrial revolution and Renaissance
passed India by. Before Ramanujan, the only noteworthy mathematician was
Sawai Jai Singh II, who founded the present city of Jaipur in 1727 A.D. This
Hindu king was a great patron of mathematicians and astronomers. He is known
for building observatories (Jantar Mantar) at Delhi, Jaipur, Ujjain, Varanasi
and Mathura. Among the instruments he designed himself are Samrat Yantra,
Ram Yantra and Jai Parkash.
Well known Indian mathematicians of 20th century are:
Shreeram Shankar Abhyankar
Shreeram Shankar Abhyankar was born in 1930, and is an Indian
mathematician known for his contributions to algebraic geometry. He is the
Marshall Distinguished Professor of Mathematics and Professor of Computer
Science and Industrial Engineering at Purdue University. His name is associated
with Abhyankar's conjecture of finite group theory.
He was born in a Maharashtrian koknastha Brahmin family. He earned his B.Sc.
from Bombay University in 1951, his A.M. at Harvard University in 1952, and his
Ph.D. at Harvard in 1956. His thesis, written under the direction of Oscar Zariski,
was titled Local uniformization on algebraic surfaces over modular ground fields.
Before going to Purdue, he was an associate professor of mathematics at Cornell
University. He was appointed the Marshall Distinguished Professor of
Mathematics in 1967.
His research topics include algebraic geometry (particularly resolution of
singularities), commutative algebra, local algebra, valuation theory, theory of
functions of several complex variables, quantum electrodynamics, circuit theory,
invariant theory, combinatorics, computer-aided design, and robotics. He
popularized the Jacobian conjecture.
His current research is in the area of computational geometry and algorithmic
Samarendra Nath Roy
December 11, 1906
Dhaka, Bangladesh, (erstwhile East Bengal)
July 23, 1964
Jasper, Alberta, Canada
Residence India , U.S.
Nationality Indian- American
Indian Statistical Institute
University of North Carolina, Chapel Hill
University of North Carolina, Chapel Hill
Doctoral advisor Prasanta Chandra Mahalanobis
Known for multivariate analysis
Samarendra Nath Roy or S. N. Roy ) (born 1906 in Dhaka, East Bengal – 1964)
was a Bengali Indian scientist, mathematician and an applied statistician. He was
the first of two children of Kali Nath Roy and Suniti Bala Roy . His father, Kali
Nath Roy was a freedom fighter and the Chief Editor of the newspaper TRIBUNE
Prof. Roy had a brilliant academic career. He secured first division in the
Matriculation Examination in 1923. He came first in the Intermediate Science
(Higher Secondary) Examinations in 1925. He also became first class first in
both the B.Sc. Mathematics (Honours) from Presidency College, Kolkata,
University of Calcutta in 1928 and the M.Sc. examinations from the University of
Calcutta in 1931 .
At that time Professor P. C. Mahalanobis was the director of the new (1931)
Indian Statistical Institute. Several talented young scholars including J. M.
Sengupta, H. C. Sinha, Raj Chandra Bose, S. N. Roy, K. R. Nair, K. Kishen and
C. R. Rao, joined to form an active group of statisticians under Prof. Mahalanobis.
S. N. Roy was one of the very early students of Prof. Prasanta Chandra
Mahalanobis, who initiated some of the early works in Statistics . He was well
known for his pioneering contribution to multivariate statistical analysis, mainly
that of the Jacobians of complicated transformations for various exact
distributions, rectangular coordinates and the Bartlett decomposition . His
dissertation included the Post master's work at the Indian Statistical Institute
where he worked under Mahalanobis.
It was Bose who first went to the United States as a visiting professor at Columbia
University and the University of North Carolina, Chapel Hill in 1947. Roy later
joined him at the University of North Carolina Chapel Hill and later became
Professor of Statistics. S. N. Roy had 15 doctorate students there from 1950 till
1963 . To commemorate his Birth Centenary an International Conference on
quot;Multivariate Statistical Methods in the 21st Century: The Legacy of Prof. S.N.
Royquot; was held at Kolkata, India during December 28-29, 2006  . The Journal of
Statistical Planning and Inference published a special Issue for celebrating of the
Centennial of Birth of S. N.
D. D. Kosambi
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For other persons named D. D. Kosambi, see D. D. Kosambi (disambiguation).
D. D. Kosambi
July 31, 1907
June 29, 1966
Occupation Mathematician and Marxist Historian
Damodar Dharmananda Kosambi (July 31, 1907 – June 29, 1966) was an
Indian mathematician, statistician, historian, and polymath who contributed to
genetics by introducing Kosambi's map function. He is well-known for his work
in numismatics and for compiling critical editions of ancient Sanskrit texts. His
father, Dharmananda Damodar Kosambi, had studied ancient Indian texts with a
particular emphasis on Buddhism and its literature in the Pali language. Damodar
Kosambi emulated him by developing a keen interest in his country's yesteryears.
Professor Kosambi was also a historian of ancient India who employed the
historical materialist approach in his work. He was critical of the policies of then
Prime Minister Jawaharlal Nehru, which, according to him, promoted capitalism
in the guise of democratic socialism. He was an enthusiast of the Chinese
revolution and its ideals, and, in addition, a leading activist in the World Peace
Movement. In the opinion of the historian Irfan Habib, quot;D. D. Kosambi and R.S.
Sharma, together with Daniel Thorner, brought peasants into the study of Indian
history for the first time