The Indian mathematician Srinivasa Ramanujan Aiyangar (1887-1920) is best known for his work on hypergeometric series and continued fractions.

# Srinivasa Ramanujan Aiyangar

Srinivasa Ramanujan, born into a poor Brahmin family at Erode on Dec. 22, 1887, attended school in nearby Kumbakonam. By the time he was 13, he could solve unaided every problem in Loney's *Trigonometry,* and at 14 he obtained the theorems for the sine and the cosine that had been anticipated by L. Euler. In 1903 he came upon George Shoobridge Carr's *Synopsis of Elementary Results in Pure and Applied Mathematics.* The book, its coverage reaching 1860, opened a whole new world to him, and he set out to establish the 6,165 theorems in it for himself. Having no contact with good books, he had to do original research for each solution. Trying to devise his own methods, he made some astounding discoveries, among them several new algebraic series.

Ramanujan became so absorbed in mathematics that when he entered the local government college in 1904 with a merit scholarship, he neglected his other subjects and lost the scholarship. Despite two later attempts, he never qualified for the first degree in arts. Ramanujan married in 1909, and while working as a clerk he continued his mathematical investigations; in 1911 he started to publish some of his results.

In January 1913 Ramanujan sent some of his work to G. H. Hardy, Cayley lecturer in mathematics at Cambridge. Hardy noticed that whereas Ramanujan had rediscovered, and gone far beyond, some of the latest conclusions of Western mathematicians, he was completely ignorant of some of the most fundamental areas. In May the University of Madras gave Ramanujan a scholarship.

In 1914 Ramanujan went to Cambridge. The university experience gave him considerable sophistication, but his mind, by this time somewhat hardened, generally continued to work according to the old pattern, in which intuition played a more important role than argument. In Hardy's opinion, if Ramanujan's gift had been recognized early, he could have become one of the greatest mathematicians of all time. In hypergeometric series and continued fractions, "he was unquestionably one of the great masters." His patience, memory, power of calculation, and intuition made him the greatest formalist of his day. But his passionate, prolific, and in some ways profound work in the theory of numbers and his work in analysis were seriously marred by misdevelopment.

In 1918 Ramanujan was elected a fellow of the Royal Society and a Fellow of Trinity College, Cambridge. He died on April 26, 1920.

## Further Reading on Srinivasa Ramanujan Aiyangar

Godfrey Harold Hardy and others, eds., *Collected Papers of Srinivasa Ramanujan* (1927), and Hardy's *Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work* (1940) include biographical material. Shiyali Ramamrita Ranganathan, *Ramanujan: The Man and the Mathematician* (Bombay, 1967), is a disappointing biography. Scientific American, *Lives in Science* (1957), and James Roy Newman, *Science and Sensibility* (2 vols., 1961), have useful accounts of Ramanujan's life.

## Additional Biography Sources

Abdi, W. H. (Wazir Hasan). *Toils and triumphs of Srinivasa Ramanujan, the man and the mathematician,* Jaipur: National, 1992.

Kanigel, Robert. *The man who knew infinity: a life of the genius Ramanujan,* New York: Washington Square Press, 1992, 1991.

Nandy, Ashis. *Alternative sciences: creativity and authenticity in two Indian scientists,* New Delhi: Allied, 1980.

Rajagopalan, K. R. *Srinivasa Ramanujan,* Madras: Sri Aravinda Bharati, 1988.

*Srinivasa Ramanujan (1887-1920): a tribute,* Madras: Macmillian India, 1988, 1987.

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