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- 1. 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 school. 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.
- 2. 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
- 3. 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 mathematicians.
- 4. Bhaskara (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
- 5. 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.
- 6. 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 algebraic geometry. S.N. Roy Samarendra Nath Roy December 11, 1906 Born Dhaka, Bangladesh, (erstwhile East Bengal) July 23, 1964 Died Jasper, Alberta, Canada Residence India , U.S. Nationality Indian- American Fields Mathematician Indian Statistical Institute Institutions University of North Carolina, Chapel Hill Calcutta University Alma mater University of North Carolina, Chapel Hill Doctoral advisor Prasanta Chandra Mahalanobis Known for multivariate analysis
- 7. 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 [1]. His father, Kali Nath Roy was a freedom fighter and the Chief Editor of the newspaper TRIBUNE [2] . 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 [1]. 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 [3]. 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 [4]. 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 [5]. 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 [6] . The Journal of Statistical Planning and Inference published a special Issue for celebrating of the Centennial of Birth of S. N. D. D. Kosambi From Wikipedia, the free encyclopedia Jump to: navigation, search For other persons named D. D. Kosambi, see D. D. Kosambi (disambiguation). D. D. Kosambi
- 8. July 31, 1907 Born Kosben, Goa June 29, 1966 Died Pune 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

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