Thread

1. glimshe · 1789815923 · focus · HN ↗

   It would be interesting to see what would happen if we had two competing mathematical institutes, a sort of First/Second Foundations:

   1) Rejection of AI for anything but trivial applications while still using computers at their full capacity. Researchers would ensure full human understanding of proofs and methods. This Institute believes on Math as a process of discovery, Mathematicians as explorers/poets/storytellers and not proof machines.

   2) Unrestricted, all-embracing use of the latest AI, including potentially research in creating even better AIs as part of the program. These researchers would be okay with not understanding proofs if verified to be correct. This group is focused on rapid problem resolution and believes Mathematicians are theorem creators and provers.

   After X years (100?), which one would advance Mathematics and humanity the most (we'd need to define "advance")?

   1. itsalwaysgood · 1789816672 · focus · HN ↗

      Mathematicians worry about proofs and the intrinsic value of something as elusive as 'understanding'. They are deeply ingrained in the study, deeply concerned with anything effecting the field. Yet they're still emotional beings looking for beauty and meaning in life that might come from an understanding how the universe works purely from a math perspective. I'm glad Mathematicians exist, I certainly can't do that type of work.

      And I trust their results: technology wouldn't be possible without advancing our understanding of the world in various fields, including math.

      Your idea sounds great for the Mathematicians.

      There's a more pragmatic view though, and unrelated to proofs themselves: does understanding a proof help us to advance Humanity in some way?

      Do we have better lives afterwards? What if we give up understanding proofs and focus only on results.

      In other words, if an AI solves a problem for you, but you don't understand how it works, should you continue building anything on top?

      I suppose the results are truly what matter. If AI solved cancer, disease, anything that lowers quality of life, but you have no idea how it did it: is that good enough?

      Your second approach seems good to help figuring out results from both theory and application of math to solve problems.

      But also, what if there is no true beauty in Math, the way Dirac and Einstein wanted?

      What if these AI brute force proofs are all that's left?

      1. bonoboTP · 1789830721 · focus · HN ↗

         > If AI solved cancer, disease, anything that lowers quality of life, but you have no idea how it did it: is that good enough?

         A lot of medicine is already like this. Shown to work in clinical trials, no complete end to end mechanism understood. They still get approved if the empirical results are strong.

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