Srinivasa Ramanujan
“His leaps of intuition confound mathematicians even today, seven decades after his death. His papers are still plumbed for their secrets. His theorems are being applied in areas—Polymer chemistry, computers, even (it has recently been suggested) cancer—scarcely imaginable in his lifetime. And always the nagging question: What might have been, had he been discovered a few years earlier, or lived a few years longer?”
To most Tamil-speaking Indians, this passage from the prologue to “The Man Who Knew Infinity”, by American author Robert Kanigel, will bring instant recognition of the subject: the mathematical genius Srinivasa Ramanujan, who was born into a poor brahmin family on December 22, 1887 at Erode, a small town in the heart of Tamil Nadu, and ‘discovered’ by English mathematician G H Hardy.
Ramanujan’s story was a fairytale, but a flawed one, with a tragic and an abrupt end, brought about by tuberculosis, which claimed the genius’ life at the age of 32. His was an untamed, intuitive, mathematical gift that enabled him to arrive at complex theorems even in his teen years.
All through his school years, Ramanujan walked off with every conceivable merit certificate and scholastic prize. The headmaster of the school once introduced him to the audience at a prize-giving ceremony, as “a student who, were it possible, deserved higher than the maximum marks.”
An innocuous book by George Shoobridge Carr, “A Synopsis of Elementary Results in Pure and Applied Mathematics,” changed Ramanujan’s life forever. This was a compendium of over 5000 equations which Ramanujan first came across in 1903, in his final year at school. Whatever its effect on other students, in Ramanujan, the book “ignited a burst of fiercely single-minded intellectual activity”, something that in time became an all-engulfing passion for mathematics.
This, naturally, led to untold trouble for the young scholar, who started to fail examination after examination, as a result of his obsession with maths that made him spend every waking moment on that subject to the exclusion of all other subjects. As a student of Kumbakonam Government College, and later, Pachaiyappa’s College, Madras, he failed
in all exams other than maths, and lost the scholarships he had won earlier. This ironically led to a five-year period during which he was totally free to pursue his passion, because his college had flunked him, and he had nothing else to do. Married in 1908, he was supported for a while by Ramachandra Rao, civil servant, and secretary of the Indian Mathematical Society, whom Ramanujan’s notebooks impressed considerably with their originality.
It was while he was a clerk in the Port Trust that Ramanujan started corresponding with British mathematicians, sending them some of his original work, especially in the infinite series of numbers. After a couple of rejections from bewildered mathematicians who did not know whether their exotic correspondent was a genius or an idiot savant, Ramanujan struck pay dirt with G H Hardy, a 35-year-old mathematician who was “turning English mathematics on its ear.” His letter read:
Dear Sir,
I beg to introduce myself as a clerk in the accounts department of the Port Trust Office at Madras on a salary of only £ 20 per annum. I am now about 23 years of age. 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.”
Third time lucky, Ramanujan was able to convince Hardy enough of his genius for the English “aristocrat of the intellect” to go to great trouble to bring him over to England, and pass him through the academic rigours that his inspired solutions had hitherto lacked.
G H Hardy
In Cambridge University, Ramanujan “was a happy man, revelling in the mathematical society
he was entering and idolised by the Indian students.” He had enough money and freedom from financial worry to pursue maths to his heart’s content. “In this old town of cobbled walks, grassy courts, and medieval chapels, whole universes away from Madras, Ramanujan had found a kind of intellectual nirvana.”
In that rarefied academic atmosphere, Ramanujan bloomed as a mathematician, though the First World War, tuberculosis and treatment at sanitaria interfered with his progress, especially as there were few mathematicians now available for him to work along with. He was elected a Fellow of the Royal Society of Mathematicians and a Trinity Fellow, high honours indeed for someone who rose from such a humble background.
Ramanujan returned to India in 1919, to have better chances of recovery in the warm climate of his native state. But on April 26, 1920, he died at Chetpet, Madras, now reduced to skin and bones, with his wife Janaki by his side. “It was always maths… Four days before he died, he was scribbling,” his wife recalled later.
Hardy, mentor, friend, maths partner, paid this tribute to Ramanujan: “He would have been a greater mathematician if he had been caught and tamed a little in his youth; he would have discovered more that was new, and that, no doubt, of greater importance. On the other hand, he would have been less of a Ramanujan, and more of a European professor, and the loss might have been greater than the gain.”
“Once, in (a) taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, “rather a dull number,” adding that he hoped that wasn’t a bad omen.
“No, Hardy,” said Ramanujan. “It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.”
Finding numbers that were the sum of one pair of cubes was easy. For example, 23 + 33 = 35. But could you get to 35 by adding some other pair of cubes? You couldn’t. And as you tried the integers one by one, it was the same story. One pair sometimes, two pair never—never, that is, until you reached 1729, which was equal to 123 + 13, but also 103 + 93.
How did Ramanujan know? It was no sudden insight. Years before, he had observed this little arithmetic morsel, recorded it in his notebook and, with that easy intimacy with numbers that was his trademark, remembered it.”
Reproduced from The Man Who Knew Infinity by Robert Kanigel.