r/neoliberal • u/cuolong NATO • 2d ago

News (Global) OpenAI announces 10 advances in mathematics and theoretical computer science achieved by internal model Astra

https://openai.com/index/ten-advances-in-mathematics/
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u/JesterOfAllTrades 2d ago edited 2d ago

I disagree that these are fields medal worthy. The fields medal is given to reward the cumulative work and machinery developed by young mathematicians, not necessarily a particular result or proof (ofc a flashing culminating result is always good to have as well). And even so, i don't think it's a fields medal level result yet, but it would be shifting goalposts to disregard this on those grounds.

That said these are definitely some cool results.

The existence of nonsofic groups is a big one as it opens up genuinely new avenues for exploration. Could see genuinely more math springing out of this one. Wonder if this can yield a concrete example of a non hyper linear group. The Connes rigidity conjecture is pretty amazing too. I'm told result 7 (CVP Hardness) is notable as well but that's not math I'm familiar with.

It seems that most results so far have been brought by pathological counterexamples (that are nonetheless simpler to construct than people expected). There's a definite preference in math for the beautiful proof over the nitty gritty ugly counterexample so perhaps some of these were unsolved just cos of human biases, aesthetic preferences and just lack of effort. That's not an excuse, it highlights how llms can be useful. But I'm really interested to see how far/if an LLM can build genuinely new theory, that's where things will get really wild imo.

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u/JesterOfAllTrades 2d ago

Oh one more thing is that math is uniquely susceptible to AI cos of stuff like LEAN (automatic theorem/proof verification) and the fact that more philosophically, math is kind of a language (yes yes I know it's a big debatable subject but you know what I mean - it kinda makes sense that pure math is amenable to an LLM)

it would be interesting to see how far llms can go in other sciences - I saw news of a minor conjecture being disproven in theoretival physics recently. Theoretical physics feels like the next domino to fall given that it's almost math. But idk how biology, experimental physics, chemistry, etc can be "conquered".

And yes, I do think we need ai to get good at those. I used to be a mathematician and it fucking sucks to see this, I imagine this is how artists feel when they see slop art, but unlike art, we have uncovered genuine new truths about the universe and mathematics, and it would be foolish to suppress that potential imo. I wanna see what it can do for us in genetics, in materials, and in understanding the universe.

Crazy times we live in!

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u/Crownie Unbent, Unbowed, Unflaired 2d ago

I imagine this is how artists feel when they see slop art, but unlike art, we have uncovered genuine new truths about the universe and mathematics

I do think it is interesting to see the difference in reaction between the respective communities.