4 ms·

i think id almost worry more that ai can solve problems in latent space that it cant translate back to tokens because decoding ruins it, and that we wont be abl

by 8note 2mo ago

i think id almost worry more that ai can solve problems in latent space that it cant translate back to tokens because decoding ruins it, and that we wont be able to come up with concepts that we can map to properly decode those solutions in a way people understand

pas 2mo ago
... what is understanding of mathematics anyway? if some AI result helps a mathematician to solve more problems I would say then that it gave them some understanding, but just as there are proofs that span hundreds of pages it's likely that soon proofs will be long Lean programs and studying them will be part of mathematics, just as studying Go played by AI. (see the open (Lean) label for Erdos problems https://mathstodon.xyz/@tao/116987866420438091 https://mathstodon.xyz/@tao/116987866420438091)
- QwenGlazer9000 2mo ago
  https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e... This blog post talks in depth about what you're talking about. It may interest you. It even talks about the future where math proofs are just Lean programs, and why that won't necessarily be a good thing. It's worth a read, even if it's long AF.
  - pas 2mo ago
    I have complicated feelings regarding academia, and in general IMHO it's way past due to start focusing on quality instead of hype. who was first to some kind of novelty? who cares. someone did something but no one can replicate it? intentionally wasting public money. fraud by any other name. "science" wouldn't move slower if we would build more robust data generating processes. of course, since usually it's hard to judge quality academia uses proxies. not to mention that the people who could usually are also live inside fancy glassware. and it would be a shame to rock the boat. ... but math is doubly special, because we accepted that it doesn't matter (until it does, but then it's called cryptography and logistics network optimization and high frequency trading, and machine learning), and how long a problem stays unsolved was quite a good proxy. still, if AI solves the easy ones we can finally have fun with the hard ones!

by 8note 2mo ago

pas 2mo ago

... what is understanding of mathematics anyway? if some AI result helps a mathematician to solve more problems I would say then that it gave them some understanding, but just as there are proofs that span hundreds of pages it's likely that soon proofs will be long Lean programs and studying them will be part of mathematics, just as studying Go played by AI. (see the open (Lean) label for Erdos problems https://mathstodon.xyz/@tao/116987866420438091 https://mathstodon.xyz/@tao/116987866420438091)

QwenGlazer9000 2mo ago
https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e... This blog post talks in depth about what you're talking about. It may interest you. It even talks about the future where math proofs are just Lean programs, and why that won't necessarily be a good thing. It's worth a read, even if it's long AF.
- pas 2mo ago
  I have complicated feelings regarding academia, and in general IMHO it's way past due to start focusing on quality instead of hype. who was first to some kind of novelty? who cares. someone did something but no one can replicate it? intentionally wasting public money. fraud by any other name. "science" wouldn't move slower if we would build more robust data generating processes. of course, since usually it's hard to judge quality academia uses proxies. not to mention that the people who could usually are also live inside fancy glassware. and it would be a shame to rock the boat. ... but math is doubly special, because we accepted that it doesn't matter (until it does, but then it's called cryptography and logistics network optimization and high frequency trading, and machine learning), and how long a problem stays unsolved was quite a good proxy. still, if AI solves the easy ones we can finally have fun with the hard ones!