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I think GP is conflating Maths with Pure Maths. While I’m sure there is new ground to break in Pure Maths, I would agree that it’s getting harder and harder. H
by laingc 4y ago
I think GP is conflating Maths with Pure Maths. While I’m sure there is new ground to break in Pure Maths, I would agree that it’s getting harder and harder.
However, as you note, in Applied Maths there are more unsolved problems than you could address with a million researchers.
A physicist or pure Mather social looks at Navier-Stokes and says, “Oh, we know how that works, nothing to do there I guess”, whereas the applied mathematician looks at it and goes, “holy cow, this could keep my entire department busy for the rest of our natural lives”.
- wrp 4y agoVery much so. Also, there is the gain from applying new tools to discover new features of old, "boring" problems.
- kaashif 4y ago> A physicist or pure Mather social looks at Navier-Stokes and says, “Oh, we know how that works, nothing to do there I guess” I don't know if that's the best example, it's one of the Millennium Prize problems to prove that smooth solutions always exist to the Navier-Stokes equations. Pure mathematicians do, by and large, still consider proving the existence of things to be "something". Maybe I'm misunderstanding what you're saying here.
- skellington 4y agoHe was simplifying for clarify, but what he said was just another form of what the person above him said which was: >> no matter what problem you can think of, either it has already been solved to the highest level of abstraction, or it's an unsolved and famous problem, or not worthwhile/trivial. << So, Millennium Prize is an unsolved and famous problem like Reimann Hypothesis, etc..