OpenAI published 722 mathematical research papers generated by an internal unreleased frontier model on GitHub, covering number theory, algebraic geometry, and other areas, with some including Lean formal proofs. Mathematicians say it could take years to understand the results, verification has become a new bottleneck, and some early-career researchers' projects have been disrupted.
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OpenAI released 722 mathematical results generated by an internal unreleased frontier model on GitHub in one go, of which only about 300 core results have completed formal verification. The real question isn't whether AI can do math, but who bears the cost of verification, explanation, and absorption when output speed exceeds understanding speed.
OpenAI publicly released 722 mathematical research results generated by an internal unreleased frontier model on GitHub, covering number theory, algebraic geometry, analysis, combinatorics, and other areas, with some results accompanied by Lean formal proofs. This is one of the few undisputed facts in this event.
But after the release, the first question the math community faced was not "are these results correct?" but "what are these results?" Several researchers said that just reading through the roughly 40-page table of contents and abstracts took nearly an hour. Álvaro Lozano-Robledo, a mathematics professor at the University of Connecticut, said that merely browsing the full list of abstracts was already overwhelming.
The Verge interviewed over 30 mathematicians about this, who described the impact with words like "shocking, suffocating, unprecedented, dreamlike, simply crazy." Researchers generally agree that merely understanding what OpenAI released this time could take years.
Here a structural misalignment appears: the speed at which AI produces new mathematics is beginning to exceed the speed at which the math community can understand, verify, and absorb mathematics. The release is one-time, but digestion accumulates year by year.
OpenAI stated that among over 700 manuscripts, only 300 core results have completed formal verification, about 42%, and said it will continue updating the repository as more formal proofs are obtained. As of the time of reporting, less than half of these manuscripts have completed formal verification.
Multiple mathematicians complained to The Verge about insufficient formal verification coverage, especially given the enormous number of results. They emphasized that even if a result comes with Lean code, evaluation does not mean it can be completed immediately—researchers still need to further check: does this formal proof actually prove the conclusion claimed in the paper, or does it only prove a related but not fully equivalent proposition?
Kevin Buzzard, a mathematics professor at Imperial College London, provided a concrete slice. In his field of algebraic number theory, he found many relevant theorems, but only about six results stood out at first glance, and almost none of these appeared to have been formally verified in Lean. His situation thus became: either read this potentially incorrect material, or wait for others to read it first, or wait for someone to formalize it before determining correctness.
Insufficient verification is not an abstract concern. Researcher Fan Nie said that when they used their self-built verification system OSVerify to check OpenAI's October 4 version of "Global quantum geometric Langlands at irrational level," they found two major issues, one of which the system also proposed a fix for. This suggests a new paradigm: AI generates proofs, and another AI system finds errors and patches them.
This article is based on Machine Heart's account of The Verge's report. Among these, OpenAI releasing 722 results, the formal verification ratio being less than half, OpenAI not disclosing the model and prompts, and AGMAI's suggestions being partly adopted are verifiable release facts; while Buckmaster's claim about research paths being destroyed, Buzzard's claim that only about six results stood out in algebraic number theory, Hassett's claim that the paper was difficult to understand, and Lichtman's claim about dozens of Fields Medal-level results are all personal judgments or accounts by the interviewed mathematicians, and this article treats them as source claims rather than equating them with confirmed conclusions. The proportion of these results that are truly correct, whether they cover others' existing work, and whether they create a new paradigm are all currently undetermined.
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