Page 19 - Ramanujan Yatra

Ramanujan
YATRA
10
Kanigel describes Ramanujan’s style of working: “...And work it was-in expressing mathematical entities, performing operations on them, trying special cases, applying existing theorems to new realms. But some of the work, too, was numerical computation. ‘Every rational integer was his personal friend,’ someone once said of Ramanujan; as with friends, he liked numbers, enjoyed being in their company. Even in the published notebooks, you can see Ramanujan giving concrete numerical form to what others might have left abstract-plugging in numbers, getting a feel for how functions ‘behaved.’ Some pages, with their dearth of l’s and j(x)’s, and their profusion of 61s and 3533s, look less like mathematical treatise, more like the homework assignment of a fourth-grader. Numerical elbow grease it was. And he put in plenty of it. One Ramanujan scholar, B.M. Wilson, later told how Ramanujan’s research into number theory was often “preceded by a table of numerical results, carried usually to a length from which most of us would shrink.”
“From which most of us would shrink.” There’s admiration there, but may be a wisp of derision too, as if in wonder that Ramanujan, of all people, could stoop so willingly to the realm of the merely arithmetical. And yet, Ramanujan was doing what great artists always do-diving into his material. He was building an intimacy with numbers, for the same reason that the painter lingers over the mixing of his paints, or the musician endlessly practices his scales.”
G.H. Hardy writes about how Ramanujan worked:
“He worked far more than the majority of modern mathematicians, by induction from numerical examples. All his congruence properties of partitions, for example, were discovered in this way. But with his memory, his patience, and his power of calculation, he combined a power of generalization, a feeling for form, and a capacity for rapid modification of his hypotheses, which was often really startling, and made him in his peculiar field, without a rival in his day....
...His memory, and his powers of calculation, were very unusual, but they could not reasonably be called ‘abnormal’. If he had to multiply two large numbers, he multiplied them in the ordinary way, he would do it with unusual rapidity and accuracy, but not more rapidly or more accurately than any mathematician who is naturally quick and has the habit of computation...
...It was his insight into algebraical formulae, transformation of infinite series, and so forth that was most amazing. On this side, most certainly, I have never met his equal, and I can compare him only with Euler or Jacobi.”...
It is evident that Ramanujan’s extraordinary achievements were based not only on brilliance but on years of intense and single-minded preparation. This preparation was entirely by self study. Therefore, to understand better the