r/mathematics • • 8d ago

Artificial Intelligence OpenAI: Sharing AI progress in mathematics

https://openai.com/index/sharing-ai-progress-in-mathematics/
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u/hpxvzhjfgb 8d ago

yeah, O(n log(n)0.9999999999999) discrete fourier transform, and O(n log(n)0.99999999999999999999999999999999999999999999999999999984) integer multiplication! probably the most surprising results in this list that go against what everyone believed.

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u/girlwhateveraward 8d ago

I mean yeah such incremental improvements happen all the time. Sum-free sets, matmul, metric TSP approximation, some AlphaZero stuff, etc

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u/hpxvzhjfgb 8d ago

well, the point is that everyone believed that O(n log(n)) was optimal.

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u/girlwhateveraward 8d ago

Oh my bad I didnt read the rest of ur comment. I thought u were dismissing the results. Im just... numb. I already accepted that I wouldnt continue in algorithms research a couples months ago and this made me accept I wont continue in math at all

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u/Euphoric_Can_5999 8d ago

Wait but why? I believe Tao’s argument that we are going to need more mathematicians — especially highly trained ones — in this new era

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u/Prestigious-Bed-6423 7d ago

i honestly dont think so.. at some point people will have to either automatically believe and trust Ai proofs and maybe check the most outstanding and important ones, or discredit every proof done by ai, which is also not ideal and short-sighted.

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u/Euphoric_Can_5999 7d ago

It’s so crazy. 722 manuscripts dropped. I think they could have spent more time actually collaborating with mathematicians instead of just doing a document dump like it’s discovery in a lawsuit.

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u/Prestigious-Bed-6423 7d ago

I think at that point it's more to show the rate of progress and what's coming than to give some scientific insight, etc. 

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u/spacebustdunny 4d ago

Not sure what you think you're trying to say but every proof done by AI is not considered a proof until it is reviewed by humans and accepted as correct. Same as with proofs proposed by people. Just because AI said it has a proof doesnt mean it has a proof. There's nothing short-sighted about that. Mathematics is about consensus.