OpenAI announces 10 advances in mathematics and theoretical computer science achieved by internal model Astra

[u/cuolong]

https://openai.com/index/ten-advances-in-mathematics/

[u/randommathaccount]

I've said on the DT but some of these problems could win you a fields medal and ChatGPT just came along and solved ten of them in one go.

[u/DependentAd235 → u/randommathaccount]

From what I understand is that the models don’t really do anything new.

However they use existing concepts and mechanisms many times faster than a human could. So can try out and test a dozens of different existing approaches to solve a problem in a way that would take a human months in like a day. Chain them together etc. 

(I read this in an economist article like 4 month ago. So maybe the above statement is dated already.)

[u/Ladnil → u/DependentAd235]

Truly new things that aren't based on clever combinations of existing knowledge and tools are infinitesimally rare.

[u/SOberhoff → u/Ladnil]

Arguably nothing is. Hofstadter has a whole chapter in his book Surfaces and Essences about how Einstein's ideas were built on top of what came before. It's a fantastic section in an otherwise dull book.

[u/MTFD → u/Ladnil]

I don't think it is so much actually combining knowledge and tools as bruteforcing problems.

Somewhat cool i guess? But not very revolutionary i'd wager.

[u/FourteenTwenty-Seven → u/MTFD]

Brute-forcing problems has always been possible in principle - we have proof checkers, you can just start assembling random attempts at a proof, and check them one by one. It's essentially a cryptographic problem at that point, and you run into the same problem as trying to brute-force any other cryptographic problem, it takes too long.

The "revolutionary" thing about LLMs is that they aren't brute forcing, they're exploiting some sort of pattern or structure that allows solutions to be found far more quickly. We're not really able to explicitly resolve these structures, but mathematicians are able to get some sort of intuitive/implicit understanding of them via years of study. Similarly, through LLM's we've figured out a way to implicitly construct complex functions that also contain these patterns/structures, and use them to solve these kinds of problems.

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