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I disagree with this scarcity point of view. Concrete example: Navier-Stokes. I don't make any claims about the truth of the announcement of the proof. But for
by encyclopediai 5d ago
I disagree with this scarcity point of view.
Concrete example: Navier-Stokes. I don't make any claims about the truth of the announcement of the proof. But for the sake of the argument le't just suppose we know now that there is a smooth solution with smooth boundary and initial data which blows out in finite time.
Navier-Stokes is the simplest among evolution problems for continuum media, because it has maximal material symmetry (that's the mathematical meaning of a fluid).
If this is solved then go to a harder one, Coulomb friction. As a real life phenomenon, friction is very interesting to explore and mathematically is much harder than NS.
So it is not like we will ever be left without things to think about.
Oh, you want another? The present AIs are things made of mathematics. I would like to understand as a mathematician how and why they can beat human problem solvers?
Is that because mathematics is in some precise, interesting sense, more "computable" than it seems?
- lelanthran 4d ago> So it is not like we will ever be left without things to think about. None of what you wrote, especially this line, makes me think you know what "eating the seed corn" means.
- encyclopediai 4d agoI feel like Randy Waterhouse in the scene where he was trying to (not) participate to a discussion at the table concerning the internet. Everybody knows what eating the seed corn means. There is no seed corn analog in mathematics. Since the fashion that mathematics is problem solving there are lots of farmers ploughing their own field, that I concede.