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In terms of deep contributions to a variety of mathematical science type fields, probably no one. People might say Terence Tao, and of course no offense to him

In terms of deep contributions to a variety of mathematical science type fields, probably no one. People might say Terence Tao, and of course no offense to him he is extraordinary smart and widely knowledged, but in my opinion he hasn't made the same level of deep contributions to mathematics let alone other fields. From what I've heard and read historically to be considered one of the "greats" so to speak you had to have full mastery of a field, either by starting it or revolutionizing it (funnily enough von Neumann was criticized for this by other mathematicians in his time). An easy example is Alexander Grothendieck, who is considered one of the top mathematicians of the 20th century. He revolutionized algebraic geometry and homological algebra. For von Neumann the most obvious field would be operator algebras. Of course the reason for mathematicians these days not being as "creative" or "revolutionary" may just be that all the low hanging fruit so to speak has already been picked, which in my view is the most obvious reason, so it's significantly harder to make deep contributions compared to times past, but it is what it is.

rybosworld 5y ago
I think things are too different today to make comparisons like that. In the last 50 years, our collective knowledge has grown at a pace that is incomparable to other periods of time. Something that falls out of that is that the open problems in a particular field are much more difficult to solve. It is also true that the knowledge is much more widespread. For instance, many CS undergrads are expected to learn game theory. What was once an advanced topic is now just part of the curriculum. Basically the common denominator has risen in a way that is much more difficult for a single mind to seem comparatively impressive.
- mjreacher 5y ago
  I agree, all the easy problems are solved so only hard ones are left, but the issue of widespread knowledge doesn't seem to be as important to me. The difficulty in a lot of fields is not for example picking up undergraduate knowledge in game theory or whatever, calculus was once an advanced topic but we can teach it to 12 year olds now, but making deep contributions to fields because as you say the easy problems have been picked so either you have to introduce a new paradigm or you have to have an ever growing amount of prerequisite material to know beforehand to contribute something new of significance.

rybosworld 5y ago

I think things are too different today to make comparisons like that. In the last 50 years, our collective knowledge has grown at a pace that is incomparable to other periods of time. Something that falls out of that is that the open problems in a particular field are much more difficult to solve. It is also true that the knowledge is much more widespread. For instance, many CS undergrads are expected to learn game theory. What was once an advanced topic is now just part of the curriculum. Basically the common denominator has risen in a way that is much more difficult for a single mind to seem comparatively impressive.

mjreacher 5y ago
I agree, all the easy problems are solved so only hard ones are left, but the issue of widespread knowledge doesn't seem to be as important to me. The difficulty in a lot of fields is not for example picking up undergraduate knowledge in game theory or whatever, calculus was once an advanced topic but we can teach it to 12 year olds now, but making deep contributions to fields because as you say the easy problems have been picked so either you have to introduce a new paradigm or you have to have an ever growing amount of prerequisite material to know beforehand to contribute something new of significance.