S. I. Ramanujan | Biography

S. I. Ramanujan was a self-taught prodigy from India. His introduction to the world of formal mathematics and subsequent fame arose from his correspondence and collaboration with the renowned British mathematician Godfrey Harold Hardy . In his short but prolific career Ramanujan made several important contributions to the field of number theory, an area of pure mathematics that deals with the properties of and patterns among ordinary numbers. Three quarters of a century after his death, mathematicians still work on his papers, attempting to provide logical proofs for results he apparently arrived at intuitively. Many of his theorems are now finding practical applications in areas as diverse as polymer chemistry and computer science, subjects virtually unknown during his own times.

Srinivasa Iyengar Ramanujan, born on December 22, 1887, was the eldest son of K. Srinivasa Iyengar and Komalatammal. He was born in his mother's parental home of Erode and raised in the city of Kumbakonam in southern India, where his father worked as a clerk in a clothing store. They were a poor family, and his mother often sang devotional songs with a group at a local temple to supplement the family income. Ramanujan received all his early education in Kumbakonam, where he studied English while still in primary school and then attended the town's English-language school. His mathematical talents became evident early on; at eleven he was already challenging his mathematics teachers with questions they could not always answer. Seeing his interest in the subject, some college students lent him books from their library. By the time he was thirteen, Ramanujan had mastered S. L. Loney's Trigonometry, a popular textbook used by students much older than him who were studying in Indian colleges and British preparatory schools. In 1904, at the age of 17, Ramanujan graduated from high school, winning a special prize in mathematics and a scholarship to attend college.

Pursues Mathematics Independently

Shortly before he completed high school, Ramanujan came across a book called A Synopsis of Elementary Results in Pure and Applied Mathematics. This book, written by British tutor G. S. Carr in the 1880s, was a compilation of approximately five thousand mathematical results, formulae, and equations. The Synopsis did not explain these equations or provide proofs for all the results; it merely laid down various mathematical generalizations as fact. In Ramanujan, the book unleashed a passion for mathematics so great that he studied it to the exclusion of all other subjects. Because of this, although Ramanujan enrolled in the Fine Arts (F.A.) course at the local Government College, he never completed the course. He began to spend all his time on mathematics, manipulating the formulae and equations in Carr's book, and neglected all the other subjects that were part of his course work at the college. His scholarship was revoked when he failed his English composition examination. In all, he attempted the F.A. examinations four times from 1904 to 1907. Each time he failed, doing poorly in all subjects except mathematics.

During these four years, and for several more, Ramanujan pursued his passion with single-minded devotion. He continued to work independently of his teachers, filling up sheets of paper with his ideas and results which were later compiled in his famous Notebooks. Carr's book had merely been a springboard to launch Ramanujan's journey into mathematics. While it gave him a direction, the book did not provide him with the methods and tools to pursue his course. These he fashioned for himself, and using them he quickly meandered from established theorems into the realms of originality. He experimented with numbers to see how they behaved, and he drew generalizations and theorems based on these observations. Some of these results and conclusions had already been proved and published in the Western world, though Ramanujan, sequestered in India, could not know that. But most of his work was original.

Meanwhile, his circumstances changed. Without a degree, it was very difficult to find a job, and for many of these years Ramanujan was desperately poor, often relying on the good graces of friends and family for support. Occasionally he would tutor students in mathematics, but most of these attempts were unsuccessful because he did not stick to the rules or syllabus. He habitually compressed multiple steps of a solution, leaving his students baffled by his leaps of logic. In July 1909 he married Janaki, a girl some ten years his junior. Keeping with local customs and traditions, the marriage had been arranged by Ramanujan and Janaki's parents. Soon afterwards, he traveled to Madras, the largest city in South India, in search of a job. Because he did not have a degree, Ramanujan presented his notebooks as evidence of his work and the research he had been conducting in past years. Most people were bewildered after reading a few pages of his books, and the few who recognized them as the work of a genius did not know what to do with them. Finally, Ramachandra Rao, a professor of mathematics at the prestigious Presidency College in Madras, reviewed the books and supported him for a while. In 1912 Ramanujan secured a position as an accounts clerk at the Madras Port Trust, giving him a meager though independent salary.

During this time, Ramanujan's work caught the attention of other scholars who recognized his abilities and encouraged him to continue his research. His first contribution to mathematical literature was a paper titled "Some Properties of Bernoulli's Numbers," and it was published in the Journal of the Indian Mathematical Society c. 1910. However, Ramanujan realized that the caliber of his work was far beyond any research being conducted in India at the time, and he began writing to leading mathematicians in England asking for their help.

Sends Letter to Hardy

The first two mathematicians he approached were eminent professors at Cambridge University, and they turned him down. On January 16, 1913, Ramanujan wrote to Godfrey Harold Hardy, who agreed to help him. Hardy was a fellow of Trinity College, Cambridge, and he specialized in number theory and analysis. Although he was initially inclined to dismiss Ramanujan's letter, which seemed full of wild claims and strange theorems with no supporting proofs, the very bizarreness of the theorems nagged at Hardy, and he decided to take a closer look. Along with J. E. Littlewood, he examined the theorems more thoroughly, and three hours after they began reading, they both decided the work was that of a genius. "They must be true because, if they were not true, no one would have had the imagination to invent them," Hardy is quoted as saying in Robert Kanigel's book The Man Who Knew Infinity.

Hardy now set about the task of bringing Ramanujan to England. In the beginning, Ramanujan resisted the idea due to religious restrictions on traveling abroad, but he was eventually persuaded to go. Ramanujan spent five years in England, from 1914 to 1919, during which time he enjoyed a productive collaboration with Hardy, who personally trained him in modern analysis. Hardy described this as the most singular experience of his life, says Kanigel in The Man Who Knew Infinity: "What did modern mathematics look like to one who had the deepest insight, but who had literally never heard of most of it"" Ramanujan was to receive several laurels during this period, including a B.A. degree from Cambridge, and appointments as Fellow of the Royal Society (at 30 he was one of the youngest ever to be honored thus) and Trinity College. But the English weather affected Ramanujan's health, and he contracted tuberculosis. In 1919 he returned to India, where he succumbed to the disease, dying on April 26, 1920.

Until the very end, Ramanujan remained passionately involved in mathematics, and he produced some original work even after his return to India. His great love for the subject and his genius are perhaps best exemplified in an incident described by Hardy in his book A Mathematician's Apology. He related that while visiting Ramanujan at a hospital outside London, where he lay ill with tuberculosis, Hardy mentioned the number of his taxicab, 1729. Hardy thought it a rather dull number. "No, Hardy! No, Hardy!" Ramanujan replied. "It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways." Kanigel reported another comment Hardy made later. He said that had Ramanujan been better educated, "he would have been less of a Ramanujan and more of a European professor and the loss might have been greater." Ramanujan himself attributed his mathematical gifts to his family deity, the goddess Namagiri. A deeply religious man, he combined his passion with his faith, and he once told a friend that "an equation for me has no meaning unless it expresses a thought of God."