Mathematicians on mathematicians

Alon Amit on Ramanujan

My personal view is that such one-on-one match-ups between this mathematician and that mathematician (or this composer and that composer, or this ballerina and that ballerina) are almost entirely pointless. There is very little to be gained from arguing who was the greatest, who was more powerful, who was better, and who had the higher IQ.

Asking if person X is "overrated" is even worse, since it depends on our gauging just how "highly rated" person X is, and then arguing whether this is in line with the "proper rating" we should ascribe to this person's "greatness". I find little value in such discussions.

Ramanujan was a rare genius of a very special kind. He made discoveries that were apparently unattainable for pretty much any other human being during his short life. Those contributions were deep and meaningful for mathematics for generations to come. There is a great deal to be learned today from studying his discoveries and marveling at his thought processes and originality. That is a discussion I'd be happy to participate in.

But was he "greater" than Gauss or Euler? I can't make sense of the question. He was born 110 years after Gauss and 180 years after Euler. Obviously the extant knowledge during their lifetimes and the things that still remained to be discovered and invented were completely different. Ramanujan's tastes and approach were completely different from those of Gauss and (to a lesser degree perhaps) Euler. Should we compare his achievements to theirs, or should we compare his achievements to what he might have achieved if he were born in the 18th century, or perhaps we should transplant Euler to the early 20th century and speculate on whether or not he would have discovered mock theta functions?

Of course in many ways Euler's work is more fundamental, but this obviously should at least in part be ascribed to the fact that he had an almost 200 year head-start, and at least in part to the fact that he lived a much longer life. Past the age of 13, Ramanujan has 20 years to create; Euler had 63 (and he made amazingly good use of each and every one of them).

(It's interesting to note, in passing, that both men did much of their work in a country far away from their birthplace; but the circumstances were so different! Euler was flourishing in the court of a Russian empress, while Ramanujan was struggling to build a life in an alien, cold England).

I don't think Ramanujan is overrated. He was a brilliant, creative and unique mathematician and person. I don't think anyone claims he was "greater" than Euler or Gauss, and if anyone does, that's just a senseless claim, not one worth judging right or wrong.