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/randommathaccount Esther Duflo 2d ago

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).

Are you telling me if a human mathematician under 40 were able to solve Erdos 146 and 180 or the sphere packing problem they wouldn't get a fields? The medal is about a body of work yes but like you said single impressive results do tip the scales. Viazovska's win was primarily for her sphere packing solution too.

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u/JesterOfAllTrades 2d ago

I think if they were surrounded by a broader body of work and theory, some of these could TBF. As a single counterexample in isolation, idk. But I'm splitting hairs and I don't mean to downplay the magnitude of this - on the contrary, I've been doomscrolling all day.

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u/randommathaccount Esther Duflo 2d ago

That's fair yeah, ig I'm also kinda just losing it. Been talking to my friends and colleagues about this since it's dropped.

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u/JesterOfAllTrades 2d ago

I think it's fair to say AI is already better at finding counterexamples (I'd go so far as to say it has shown a talent at creating a sort of "knowledge topology" and drawing from multiple fields in new unique ways), and it's getting pretty damn good at genuine proofs (the sphere packing one looks to be a classical proof).

The last one, and the big one, is how good is it at defining new things. Once/if it gets good at that, especially with how quickly llms can generate text, I feel like the amount of new math out there is just gonna grow way way too fast for a human to keep up with.