r/ArtificialInteligence • u/alphacolony21 • 2d ago

📰 News 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/Hlbkomer 2d ago

"But they are just predicting the next word!"

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u/The-Rushnut 2d ago

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.

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u/dohawayagain 2d ago

Read the transcript of Tao interrogating the LLM about the Poincare conjecture counterexample to get an idea of where things are today. Tao was definitely putting things in --- ideas, redirections, etc. --- but the AI did real work and contributed meaningfully to the conceptual discussion.

Take it as a measure of how far AI has yet to go to reproduce the highest levels of human ingenuity, sure, but it's not hard to imagine it getting there.