Thread

1. dekhn · 1789837233 · focus · HN ↗

   I have been losing interest in this proof-oriented approach into extremely abstract concepts (what seems to be the core of academic mathematics today). Obviously, proofs are very attractive because they are the closest thing we have to a universal truth (at least under the assumed axioms). Having mechanisms to reliably show a proof, and computational methods to handle complicted proofs is great.

   But.. the navier stokes proof was the last straw for me. People spent over a hundred years arguing whether a continuum approximation of a particle system would behave oddly. In the mean time, other folks went ahead and completely revolutionized the world of computational fluid dynamics (with multi-billion $$$ impact on society) by just doing better numerics (Kahn-style numerical analysis).

   Making my complaint more general: I find modern math is exploring areas that are interesting to mathematicians, but increasingly irrelevant to society. And certainly not moving us towards "human understanding". The biologists are the ones working on that, the math folks should try working with them on neuro stuff to understand how human brains can do math at all, given their architecture.

   1. magicalist · 1789841405 · focus · HN ↗

      > Making my complaint more general: I find modern math is exploring areas that are interesting to mathematicians, but increasingly irrelevant to society.

      Is it, or is it only the parts you hear about/pay attention to?

      > People spent over a hundred years arguing whether a continuum approximation of a particle system would behave oddly. In the mean time, other folks went ahead and completely revolutionized the world of computational fluid dynamics (with multi-billion $$$ impact on society) by just doing better numerics (Kahn-style numerical analysis).

      Yes, maybe famous solving famous conjectures is just trivia and trophy collecting and the real value is the intuition and techniques you develop along the way to solving them which you can then bring to bear on things like CFD.

      1. dekhn · 1789848690 · focus · HN ↗

         Mostly the parts I hear about. But I also communicate with mathematicians on a regular basis and I can see what they are working on, which is representative of the field. It's about 90% "cohomology of abstract Lie groups that morphize into string theory" and about 10% "practical thing that engineers can use to make my cell phone work better". (amusingly, although I literally made up that sentence, it turns out it's not far from something somebody worked on: "The cohomology of compact simple Lie groups and spin groups connects to string theory by providing the topological obstruction classes—specifically the first fractional Pontryagin class ...." OK, kind of emphasizing my point there.

         No, the intuition and techniques that get developed to solve the NS conjecture have little or no bearing on the practical details of doing CFD. That's a common story/thread (and I hear the same story in quantitiative biology, my area of expertise), but often times, it's just a loose justification given to justify funding.

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