4 ms·

I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy. ign

I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy. ignoring the attribution issue, there is a real concern that the process of math has been somewhat undermined. so we have a giant lean proof that shows that there is a solution to an important problem. but we didn't find the solution, and we didn't get it expressed in such a way that it helps develop the common language of mathematics, and thus isn't a very useful building block for later work (like the actual solution). the math people seem to really keep an eye on what's important, so I'm sure this isn't going to lead to fields medalists hanging around in dive bars all afternoon stretching out cheap pitchers of beer. but this is kind of a slop problem.

lelanthran 16d ago
> I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy. If advancement comes at the expense of having fewer (or no) humans left in the field, then no. They're eating the seed-corn, and you're cheering them on. Don't be so short-sighted. There's a reason farmers keep seed corn, and it's because they'd like to eat again next year. We're singing and cheering our way into an intellectual famine.
- encyclopediai 14d 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 14d 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 14d ago
      I 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.

lelanthran 16d ago

> I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy. If advancement comes at the expense of having fewer (or no) humans left in the field, then no. They're eating the seed-corn, and you're cheering them on. Don't be so short-sighted. There's a reason farmers keep seed corn, and it's because they'd like to eat again next year. We're singing and cheering our way into an intellectual famine.

encyclopediai 14d 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 14d 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 14d ago
    I 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.