Srinivasa Ramanujan (Dec. 22, 1887 - April 26, 1920)

We shall briefly sketch the life of that brilliant, self-taught mathematician, whose work contains some of the most beautiful ideas in the history of mathematics and whose life tragically ended at the age of thirty two.

Srinivasa Ramanujan was born on December 22, 1887. He belongs to a south Indian Brahmin family of Ayyangars. Srinivasa was his father's name, Komalatammal being his mother's. Namagiri was their family goddess, who, according to Ramanujan did play a vital role in his life.

After completing school, Ramanujan went to college with a scholarship. His lack of interest in other subjects and his total concentration in mathematics, created hardships for him. Everyone knew he was gifted, but that hardly sufficed to help him to continue and get a degree. The ineffective and inefficient system of education did not budge to help him continue his studies. Ramanujan ran away from home in 1905, since he was torn and miserable with the situation.

Ramanujan's intellectual eccentricities could not be understood by his parents and they got him married to Janaki in 1909, thinking that it might help. He found a job as a clerk in the Madras Port Trust and pursued his mathematics in his free time. In fact, he began to complete a notebook since in proving one formula, he discovered many others. His notebook's ranged over a vast terrain in the course of time.

Ramanujan's first research paper on Bernoulli numbers was published in 1911 in the Journal of Indian Mathematical Society. Many scholars advised him that no one in India properly understood him. In January 1913, Ramanujan wrote a letter to Professor G.H. Hardy, including some of his results, and begging Hardy's opinion regarding his ideas. The last page of Ramanujan's letter contained mathematics that Hardy, in 1913, could make nothing of it. He wrote " I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathemetician of the highest class. They must be true because, if theywere not true, no one would have the imagination to invent them". Hardy realized that the letter was the work of a genius, though not earlier. The publication of the results some years later, set off a a flurry of work by English mathematicians.

Hardy sprung into action, advising the Indian office in London of his interest in Ramanujan and of his wish to bring him to Cambridge. At first Ramanujan refused to travel to England but in the end, decided to go in 1914, which he attributed to the divine inspiration of Namagiri. It was also partly due to the help of Hardy's man, E.H.Neville. On April 14, 1914, Ramanujan arrived to England.

Together now in Cambridge, Ramanujan saw Hardy almost every day. He was productive, worked hard, and was happy. Hardy had Ramanujan's notebooks before him. Ramanujan's bulky mathematics letters, Hardy now saw represented but the thinnest sampling, the barest tip of the iceburg of what had accumulated over the past decade in his notebooks. There were thousands of theorems, page after page; they stretched on, rarely watered down by proof or explanation, almost aphoristic in their comperssion, all their mathematical truths boiled down to a line or two.

In 1921, after having been exposed to those notebooks of Ramanujan's for seven years. Hardy noted that " a mass of unpublished material " still awaits analysis. For Hardy's part, confronting the mystery of Ramanujan's mind would constitute, " the most singular experience of his life ". Ramanujan's combined power of generalization, a feeling of the form, and capacity for rapid modification of his hypotheses were startling, and made him without a rival in his day. The glory of Ramanujan was that so much came to him so readily through the divine intervention of the offices of the goddess Namagiri, as he claimed.

According to Hardy, " the limitations of Ramanujan's knowledge were as starting as its profundity" .

Here was a man who could workout modular equations and theorems of complex multiplication, to orders unheard of, whose mastery of continued fractons was, beyond that of any mathematician in the world, who had found for himself the functional equation of the zeta - function, and the dominant terms of the many of the most famous problems in the analytic theory of numbers; and he had never heard of a doubly periodic function or of Cauchy's theorem, and had indeed but the vaguest idea of what a functon of a complex variable was.

Ramanujan's isolation from his family and the intensity of his work, coupled with the English cold weather and his vegetarianism made it harder to nutritionally maintain his health. His suffering from malnutrition, was diagnosed with tubercoloiss and was admitted into a nursing home. Although Hardy was considerate, loyal, and kind to Ramanujan, unintentionally he did harm. For in the ardent hope that he had for Ramanujan to live up to his poetial, Hardy may have helped him to dig a deeper hole than Ramanujan was digging for himself.

Observing Ramanujan's failing health, Hardy pursued relentlessly his election as a fellow of the Royal would accept when his health improved.

Even though his physical body was failing and he was in serious pain, Ramanujan's intelectual vision grew proportionally keener and brigher. On January 12, 1920, he wrote to Hardy about his discovery of some very interesting functions, which he called " mock " theta functions. The mock theta functions alone, wrote Watson, are an achieveent sufficient to cause his name to be held in lasting rememberance.

On April 26, 1920, at the age of 32 Ramanujan lapsed into unconsciousness and died.

Ramanujan was a simple man. His needs were simple, and so were his manners and humor. He was persistent, hardworking and charming in his own way. He was his own man, who made himself. He simply wanted the freedom to do as he wished, to be left alone to think, to dream, to create, to lose himself in a world of his own making. In this sense, as someone said, he was " Svayambhu " that is, he had created himself.

Among Ramanujan's contemporaries, particularly his close collaborator Hardy, there was a sense of disappointement, the feeling that Ramanujan's ignorance of modern mathematics, his strange ways of doing mathematics and his premature death had diminished his achievements and therfore his influence on the future of the subject. In 1976, George Andrews, an American mathematician, came across a hundred and thirty pages of scrap paper in library at Cambridge, fillee with notes representing Ramanujan's work during the last year of his life in Madras. This is what a collborator of Andrews, Richard Askehy, had to say about what has come to be known as Ramanujan's " lost Notebook ".

The work of that one year, while he was dying, was the equivalent of a lifetime's work of a very great mathematician. What he accomplished was unbelievable. If it were in a novel, nobody would believe it.

The riches contained in the " Lost Notebook " and his earlier work are being mined with increasing success and excitement by mathematicians today. They have contributed to the creation of one of one of the most revolutionary concepts of recent theoretical physic, the superstring theory in cosmology. Also, Ramanujan's 1914 paper on " Modulus functions and approximations to pi " was employed to program a computer was employed to program a computer some time ago to evaluate pi to a level of accuracy, never attained earlier.

As Kanigel remarks, What makes Ramanujan's work so seductive, is not the prospect of its use in the solution of real world problems, but its riches, beauty and mystery its sheer mathematical loveliness.

It is to be understood that the enigmatic and creative process of Srinivasa Ramanujan, which is still covered by certain that has barely been drawn and is a treasure trove for researchers.

Source : The Origin and History of Mathematics, V.Lakshmikantham, S.Leela and J.Vasundhara Devi, Florida Institute of Technology, USA, Cambridge Scientific Publishers.