I have set myself a task that is genuinely difficult, even impossible --- to form some sort of reasoned estimate of the most romantic figure in the recent history of mathematics; a man whose career seems full of paradoxes and contradictions, who defies almost all the canons by which we are accustomed to judge one another, and about whom all of us will probably agree in one judgement only, that he was in some sense a very great mathematician.
The difficulties in judging Ramanujan are clear --- he was an Indian, I am an Englishman, and the two parties have always found it hard to understand one another. He was at best, a half-educated Indian, since he never could rise to be even a "failed B.A.". He worked for most of his life ignorant of modern European maths, and died when he was thirty and when his mathematical education had in some ways hardly begun. He published abundantly (at least 400 pages worth) but left behind even more unpublished stuff. While this work includes much that is new, about two-thirds is rediscovery, that too usually imperfect rediscovery.
Srinivasa Aiyangar Ramanujan was born in 1887 in a poor Brahmin family at Erode near Kumbakonam, a fair sized town in the Tanjore district of Tamil Nadu. His father was a clerk in a cloth-merchant's office in Kumbakonam. He was sent at seven to the local high school and stayed there nine years. By the time he was in his early teens it was common knowledge that he was more than just a brilliant student, discovering for instance the relationship between circular and exponential functions (cos a + i sin a = e^ia). This of course had been discovered by Euler before, as he found out much to his chagrin later on.
When he was sixteen he came across "A synopsis of elementary results (actually, over 6000 theorems) in pure and applied mathematics" by George Carr, . This enthusiastic book served to introduce Ramanujan to the real world of mathematics, but in a highly personal style that relegated the proofs to mere footnotes. Ramanujan went through the entire book methodically and excitedly, proving its theorems by himself, often as he got up in the morn. He claimed that the goddess of Namakkal inspired him with formulae in dreams.
Was he religious? Certainly he observed his duties as a high-caste Hindu assiduously, like being a faultless vegetarian and cooking all his food himself (after changing into his pyjamas first). And while his excellent Indian biographers (Seshu Aiyar and Ramachandra Rao) say he believed in the existence of a Supreme Being, in Kharma, Nirvana and other Hindu tenets, I suspect he was not affected by religion any more than as a collection of rules to be followed. He told me once, to my surprise, that all religions seemed to him to be more or less equally true.
Some thought, and may still think, of Ramanujan as a unintelligible manifestation of the mystic East. Far from it! He had his oddities, no doubt mostly originating from his different culture, but he was as reasonable, sane and shrewd as anyone I've met. He was a man in whom society could take pleasure, with whom one could sip tea and discuss politics or mathematics. He was a normal human being who happened to be a great mathematician.
Back to his early days. Thanks to his fine academic school record, he won a scholarship to university. But there he spent his time doing mathematics at the expense of his other subjects, which he consequently failed. His scholarship was not renewed. Further attempts to complete his degree failed. He married at 22 but could not find a university post, despite the fervent attempts of some influential Indians he had impressed with his results, Ramaswami Aiyar and his two biographers. Finally (at 25) in 1912 he found his first real job, a mundane clerical one in the Port Trust of Madras. But the damage had been done --- the years between 18 and 25 are the critical ones in a mathematician's life and his genius never again had the chance of full development. This, and not his early death, was the real tragedy, that his genius was misdirected, sidetracked and to some extent distorted by an inelastic and inefficient educational system.
But the foundations of at least a partial recovery had been laid. In 1911 he had published his first substantial paper and the following year two Britons, Sir Gilbert Walker and Sir Francis Spring secured for him a special scholarship (60 pounds a year) that was enough for a married man to live in tolerable comfort. He wrote to me in early 1913, and Professor Neville and myself got him to Britain after much difficulty in 1914. He then had three years of continuous work before falling ill in mid-1917. He was only able to work spasmodically (but as well as ever) after this, and died in 1920.
The stories, true and false, of what happened when I read the letters of an unknown Hindu clerk have been well spread --- like how I first stored them in my wastepaper basket before retrieving them for a second look, and so on. His letters contained the bare statement of about 120 theorems. Several of them were known already, others were not. Of these, some I could prove (after harder work than I had expected) while others fairly blew me away. I had never seen the like! Only a mathematician of the highest class could have written them. They had to be true, for if they were not, no one would have the imagination to invent them. A few were definitely wrong. But that only added credence to my feeling that the writer was totally honest, since great mathematicians are commoner than frauds of the incredible skill that would be needed to create such a letter.
In his favourite topics, like infinite series and continued fractions, he had no equal this century. His insight into algebraic formulae, often (and unusually) brought about by considering numerical examples, was truly amazing. But in analytic number theory, a subject he is often associated with, I do not believe he actually knew that much. He certainly contributed little of significance that was not known already. And in a subject that relied so much on proof, a subject where intuition had a bad habit of coming unstuck, he produced much that was false.
I have in the past tried to say things like "his failure was more wonderful than any of his triumphs", but that is absurd. It is no use trying to pretend that failure is something else. All we can say is that his failures give us additional, surprising evidence of his imagination and versatility. And we can respect him as one who let his mind run free, instead of keeping it under saddle and blinkers like so many others do.
But the reputation of a mathematician cannot be made by failures or by rediscoveries; it must rest primarily, and rightly, on actual and original achievement. And it is still possible to justify Ramanujan on these grounds.