OpenAI announces solutions to 10 longstanding maths problems
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- OpenAI's prototype model Astra revealed solutions to 10 longstanding mathematical problems, the most notable being a counterexample disproving the hypothesis that all countable groups are sofic—a property first described in 1999.
- Francesco Fournier-Facio at the University of Cambridge, who has studied soficity since starting his PhD in 2020, says OpenAI's solution builds heavily on prior papers by Andreas Thom and Gábor Kun from 2016 and 2019, and questions whether AI could have reached the result without that human foundation.
- OpenAI initially claimed all 10 problems had seen no progress on the main result for at least a decade, then revised the statement after Fournier-Facio called it incorrect.
- Fournier-Facio argues AI math breakthroughs so far have focused on easily checkable counterexamples rather than developing new theory, which he says has no clear verification endpoint.
- Abhishek Saha at Queen Mary University of London called the 10 solutions the most impressive display of AI mathematical prowess to date, noting some are proofs—not just counterexamples—that assemble known techniques in novel ways.
- Elon Musk tweeted the non-sofic group discovery is evidence humanity has reached the singularity, as mathematicians described adjusting to a 'radical shake-up' in their field.
Why it matters: The soficity counterexample is forcing mathematicians to confront who gets credit when AI solves longstanding problems: Fournier-Facio argues OpenAI's result leans on Thom and Kun's 2016 and 2019 work, and the company has already revised one claim about the problems' difficulty. If AI labs continue solving open problems without transparently crediting the human foundation, attribution disputes—not mathematical progress—may become the field's next battleground.
