OpenAI announces solutions to 10 longstanding maths problems — SkimNews
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- OpenAI's prototype AI model Astra produced solutions to 10 longstanding mathematical problems, ranging from high-dimensional sphere packing to quantum game theory, in what Abhishek Saha called "the most impressive display of AI mathematical prowess to date."
- The standout result is a non-sofic group—the first proven example of a group that cannot be approximated by finite permutation groups—settling a question mathematicians chased since soficity was described in 1999.
- Francesco Fournier-Facio at the University of Cambridge says Astra's soficity solution builds on 2016 and 2019 work by Andreas Thom and Gábor Kun, telling New Scientist the AI "couldn't have if not for prior human work."
- OpenAI initially claimed the 10 problems had "no progress on the main result for at least a decade" but amended the statement after Fournier-Facio complained the claim was incorrect.
- Fournier-Facio argues AI excels at finding checkable counterexamples rather than developing new theory, pointing out there is "no tick at the end" for theoretical work—raising questions about how AI companies credit prior research.
- Elon Musk tweeted the discovery was evidence humanity has reached the singularity—the point at which AI becomes self-improving toward general intelligence.
- The Astra results follow an OpenAI model cracking an Erdős conjecture in May and Claude Fable 5 finding a counterexample to the Jacobian conjecture last month, marking three major AI-led maths findings in roughly two months.
Why it matters: The first proven non-sofic group settles a 25-year mathematical question, and concurrent AI breakthroughs suggest mathematical discovery is accelerating. But Fournier-Facio's objection—that AI repackages prior human work without building new theory—means journals and universities face pressure to define credit and verification standards for AI-led results.
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