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> This is especially true in math and physics. You will find that no matter what problem you can think of, either it has already been solved to the highest leve

> This is especially true in math and physics. You will find that 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. This hasn't been my experience in fluid dynamics. There are so many places where one could apply a standard approach that people haven't. It takes some effort and experience to recognize that, but it's still true in my experience. I think what you described is probably true for sexier areas like high-energy physics, but not true for more "boring" areas like turbulent flows. Yes, turbulence is "unsolved", but that doesn't mean that useful information couldn't come from applying standard approaches to particular turbulent flows. The variety of industrially-relevant flows is quite large.

cycomanic 4y ago
I agree with you there are so many areas still vastly unexplored, fluid dynamics or the whole area of complex systems is definitely a prime example. Stephen Hawkins called his inaugural lecture "Is the End in Sight for Theoretical Physics?" suggesting that we are very close to the end of theoretical discoveries. Although less famous I would argue that prediction was just as wrong as "640kB should be enough for everyone", lots of extremely fundamental discoveries had been made since then, and we don't seem to significantly closer to a theory of everything.
- Beldin 4y ago
  He discusses in (if memory serves) "A Brief History of Time" whether we will keep on discovering ever-more accurate physical theories, or if there's a theoretical limit. The Planck scale offers a theoretical limit, so there's hope. At any rate, that is how I understood him. Not that we're nearly there, but that our current path of discovery seems finite.
  - cycomanic 4y ago
    To be honest I have not read his books, but I always had the impression from his talks that he was quite narrow minded in that he largely only meant astro/particle physics when talking about theoretical physics, ignoring many areas in the process. Also worth noting that the book came out 10 years after his lecture, so he probably revised his views during that time.
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 ago
  Very 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 ago
    He 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..
Fomite 4y ago
A huge portion of my research agenda is trying to get math and CS colleagues to apply pretty standard techniques to novel problems. If it works well, you get to push clinical science forward. Then about half the time, "This seems like a boring classification problem" turns out to be way harder than expected.

cycomanic 4y ago

I agree with you there are so many areas still vastly unexplored, fluid dynamics or the whole area of complex systems is definitely a prime example. Stephen Hawkins called his inaugural lecture "Is the End in Sight for Theoretical Physics?" suggesting that we are very close to the end of theoretical discoveries. Although less famous I would argue that prediction was just as wrong as "640kB should be enough for everyone", lots of extremely fundamental discoveries had been made since then, and we don't seem to significantly closer to a theory of everything.

Beldin 4y ago
He discusses in (if memory serves) "A Brief History of Time" whether we will keep on discovering ever-more accurate physical theories, or if there's a theoretical limit. The Planck scale offers a theoretical limit, so there's hope. At any rate, that is how I understood him. Not that we're nearly there, but that our current path of discovery seems finite.
- cycomanic 4y ago
  To be honest I have not read his books, but I always had the impression from his talks that he was quite narrow minded in that he largely only meant astro/particle physics when talking about theoretical physics, ignoring many areas in the process. Also worth noting that the book came out 10 years after his lecture, so he probably revised his views during that time.

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 ago
Very 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 ago
  He 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..

Fomite 4y ago

A huge portion of my research agenda is trying to get math and CS colleagues to apply pretty standard techniques to novel problems. If it works well, you get to push clinical science forward. Then about half the time, "This seems like a boring classification problem" turns out to be way harder than expected.