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OpenAI publishes math results from an unreleased model, with Lean proofs

The release notes explain how the results were checked and what OpenAI disclosed about how they were produced.

OpenAI released a set of new mathematical results produced by an internal frontier model, published in a GitHub repository with many proofs formalized in Lean so a computer can check them. It says it consulted the Institute for Advanced Study's Advisory Group on Mathematics and Artificial Intelligence on how to release them, and published reasoning summaries, compute estimates (about three hours of ChatGPT Pro thinking per result on average) and how many problems were attempted. OpenAI says it is working to release the model.

Read it at the source
OpenAISharing AI progress in mathematics ↗ Hacker NewsDiscussion: Sharing AI progress in mathematics ↗
Cascadic Analysis 2
UndertowWe don't completely understand why frontier models behave as they do

What hidden risk could pull against this, even if the news is good?

OpenAI shared summaries of the model's reasoning for 10 results, not the reasoning itself, from a model the public can't use yet. Lean can confirm a proof is valid; it can't show how the model found it or how often it fails.

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UndertowBenchmark scores can overstate real-world reliability

What hidden risk could pull against this, even if the news is good?

OpenAI chose which results to publish and reported how many problems were attempted. Success on selected research problems, at about three hours of top-tier compute each, says little about how the model does on an ordinary user's math.

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Rabbit Holes 1
  • Lean (proof assistant)

    After exploring Sharing AI progress in mathematics, the tool that checks these proofs is Lean (proof assistant).

    Lean is a proof assistant and functional programming language, free and open source, now supported by the nonprofit Lean Focused Research Organization.

    Wikipedia · Swim · 30 min

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