This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: Earlier this week, OpenAI published a trove of hundreds of mathematical results it claimed could "push the frontier of human knowledge." Produced largely by an unreleased artificial intelligence (AI) model, the 722 papers relate to 372 open problems covering everything from algebra and geometry to theoretical computer science. Several papers have since been retracted or amended, but the sheer scale and form of the release—variously described as a drop, a dump, a carpet bombing and a mathocalypse—have sent shock waves through the mathematical community.
Some papers claim significant advances on high-profile, long-standing problems including the Riemann hypothesis and the Birch–Swinnerton-Dyer conjecture, each of which carries a bounty of US$1 million (A$1.4 million) if solved as one of the seven Millennium Prize Problems. Why has OpenAI done this? And can we trust that the claimed solutions are correct?
Neither of these questions seems to have a particularly obvious answer. OpenAI says its motivation in releasing the huge trove of results is to "enable further progress in mathematics." However, the manner of the release is not necessarily conducive to this goal. A senior colleague of mine found one of his favorite problems among those solved and attempted to read the accompanying paper.
He told me it was so unintelligible that, had he received it as an editor at a mathematics journal, "it would have gone straight into the trash." Even OpenAI's own large language model ChatGPT (GPT-5.6 Sol, to be precise) was skeptical when I asked it, describing at least one of the high-profile results as "a serious hallucination … [which] should never be cited, submitted, or circulated as a proof without a complete expert audit." In other words, despite the groundbreaking nature of some of the results obtained, the way at least some of the accompanying papers are written is not comprehensible even to experts. OpenAI also may be seeking to move the discussion on from its last big mathematical publication. In September, the company published a controversial claimed solution to a case of the Navier–Stokes problem, another $1 million Millennium Prize Problem.
Mathematicians Tristan Buckmaster and Levent Alpöge, who had been working on the problem themselves, alleged OpenAI had accessed their data and used their ideas, then devoted some US$15 million worth of computing power to finding a solution. OpenAI has denied these allegations. One other possible broader motivation for OpenAI is the hot topic of artificial general intelligence (AGI).
This is a hypothetical type of AI that could surpass humans in basically all cognitive tasks. Mathematics—especially pure, abstract mathematics—is a discipline that largely relies on often very complex arguments to prove the truth of mathematical statements. It is often seen as a subject that is very difficult for most people.
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