The National Mathematics Day turns ten this year on December 22. The day is celebrated to commemorate the son of the soil, Srinivasa Iyengar Ramanujan. This piece is an attempt at gauging the acumen that Ramanujan possessed through the words of one of the finest and celebrated brains in mathematics, Godfrey Harold Hardy.
Though Hardy and Ramanujan were poles apart, yet they shared a bond like no other. Ramanujan was a believer, a religious one. In his often-quoted words, Ramanujan said, “An equation for me has no meaning unless it expresses a thought of God.” This makes us realize the deep-rootedness of religious beliefs Ramanujan had. G. H. Hardy, on the other hand, was an atheist. Hardy even appears on Wikipedia’s page, English Atheists, that enlists several known Englishmen who did not believe in God. This was a strange juxtaposition. Another difference between Hardy and Ramanujan was regarding their approach to the study of mathematics. Proofs were, somewhat, immaterial when it came to Ramanujan. He disliked being asked for proofs and justifications. Hardy, however, had a completely different outlook. The proof was to him, somewhat, more important than the result. Hardy wrote, “The seriousness of a theorem, of course, does not lie in its consequences, which are merely the evidence for its seriousness.” Despite these striking differences, the two nurtured a remarkably unforgettable companionship.
It appears that the bond of understanding that existed between Ramanujan and Hardy was a result of their common love for pure mathematics. Hardy loved and preferred pure mathematics to its applications. For him, the technique and the method carried more weight and deserved more appreciation than an application of a theorem. In his words, “One rather curious conclusion emerges, that pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.” Acknowledging the fact that Ramanujan was a pure, or rather a hyper-pure mathematician, Hardy did not find it hard to appreciate the kind of mathematics Ramanujan engaged himself with.
Given the fact that Hardy collaborated with Ramanujan better than anyone else, it would be safe to render that there could be no one more qualified who could have written anything on Ramanujan, more authoritatively, than G. H. Hardy. This is what Hardy wrote in his famous work, ‘A Mathematician’s Apology’: “I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, ‘Well, I have done one the thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.”
This speaks for itself. Hardy was super-refined as a mathematician, Ramanujan was hardly knowledgeable of the skills of proof; Hardy was celebrated, Ramanujan was lost like a wildflower. It would be no exaggeration to proclaim that Hardy’s discovery of Ramanujan could be considered akin to Wordsworth’s preserving of Lucy, at least through his poems. But for Hardy’s involvement and efforts, Ramanujan could have been an unknown tale or an unsung song.
Robert Kanigel, the author of Ramanujan’s biography, ‘The Man Who Knew Infinity’, wrote, “Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan, he gave 100.”
A tribute to Ramanujan better than that of Hardy’s is hard to pay. Hardy wrote about Ramanujan, “The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations, and theorems of complex multiplication, to orders unheard of, whose mastery of continued fractions was, on the formal side at any rate, beyond that of any mathematician in the world. It was impossible to ask such a man to submit to systematic instruction, to try to learn mathematics from the beginning once more. On the other hand, there were things of which it was impossible that he would remain in ignorance. So I had to try to teach him, and in a measure, I succeeded, though I obviously learnt from him much more than he learnt from me.”
The writer is Assistant Professor of Mathematics at Government Degree College Sopore. [email protected]