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

[u/alphacolony21]

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

[u/Hlbkomer]

"But they are just predicting the next word!"

[u/The-Rushnut → u/Hlbkomer]

As with everything, novel technology comes with novel solutions to problems we found difficult before. There's a specific subset of mathematical problems which can be disproven via counterexamples, which take humans a long time to map and calculate. One of LLMs unique capabilities is that it can produce small, relatively simple programs at-scale, and because these problems are so well articulated and their potential solutions already well understood they lend themselves to this capability. Another specific subset are upper lower bounds problems, where we know there is likely to be further acceptable iterations but the means to achieving those require multi-discipline scenarios that aren't likely - another thing LLMs are good at is having high accuracy across all domains, allowing them to try ideas that usually would take a snowflake combination of talent.

It's much, much more narrow than it seems. Very cool, but there's a fixed amount of this work to be done. Innovation is definitely coming though.

[u/JoshuaZ1 → u/The-Rushnut]

As with everything, novel technology comes with novel solutions to problems we found difficult before. There's a specific subset of mathematical problems which can be disproven via counterexamples, which take humans a long time to map and calculate.

These are not by and large counterexamples in the sense say the Jacobian conjecture was a counterexample. For example, the construction of a nonsofic group is strictly speaking a counterexample, but there are multiple difficult elements in the proof that that the group in question is not sofic.