People like Ramanujan are on a different planet compared to your everyday PhD working stiffs. There's smart (PhD), there's genius (Einstein, Feynman, von Neumann), and then there are freaks of nature like Ramanujan.
Ramanujan is obviously very gifted and was able to do exceptionally well given his circumstances, but to put him higher than those that you listed is wrong to me. There are many more mathematicians who solved problems that have more impact and those that started new branches of math. Ramanujan is overrated in my opinion.
I couldn't comment on the impact of his work, which anyways is evidentially still unfolding, but the WAY he seems to have worked is just bizarre - coming up with these deep baffling series formulae offered without proof. His mind seems to have worked in an extraordinary way.
It's true that the unconscious way he came about his theorems puts him in a different category to other famous names. But I wouldn't rank him as highly as Von Neumann. That man made groundbreaking results in the foundations of mathematics, pure and applied mathematics, early computer science, quantum mechanics, economics, and more. I think Von Neumann might arguably be the most significant genius of the 20th Century, paralleled in history only perhaps by the likes of Newton and Leibniz.
Einstein made a few extremely valuable insights in theoretical physics, but I'd say the sheer breadth of comparable work that Von Neumann did across multiple fields makes him more outstanding.
yes, but the contrast is striking:
Von Neumann had privileged upbringing and education
Just imagine what what Ramanujan could have been if he grew up in Von Neumann household
Do you know the saying "comparison is the thief of joy"?
It was intended to apply to oneself, but seems just as true when appreciating the genius of others. No need to diminish von Neumann, etc., AND doing so just diminishes your own credibility.
I'm not sure there's much you can do to help someone at this level, other than perhaps take away outside distractions.
It's not remotely clear how Ramanujan's mind worked, or whether he really knew himself. He seems to have been a lot more highly functioning than an idiot savant, but still operating at a level that is hard to comprehend. Was this an expression of humility or devotion by Ramanujan, or was he just expressing his own lack of understanding of how his mind worked?
There's a parallel there to Feynman, if you squint a bit. He seems to have been synaesthetic in a way that let him use the sensory part of his brain as a maths coprocessor, and he didn't understand it himself.
Feymann seems more understandable. He wanted to understand everything from first principles and derive it all himself, and spent a lifetime doing so, building himself up. He developed a huge repertoire of insights and mathematical tricks/approaches that could be brought to bear on whatever he put his mind to... It seems like he trained his mind to become what it was. The end result was of course incredible, and he would instantly or within hours see solutions to problems that colleagues had been stuck on for months.
Feynmann, like von Neumann, also seems more approachable/understandable in that he wasn't just operating at genius level, but was also a regular fun loving guy (strip clubs, bongo drums, safe hacking and all). Von Neumann and some of his Hungarian peers were famously referred to as "The Martians", but it's really Ramanujan who seems like the alien.
