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
