OpenAI's Astra solves 10 longstanding math problems
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- OpenAI's prototype Astra revealed solutions to 10 longstanding mathematical problems, spanning high-dimensional sphere packing and quantum game theory, in what one expert called the most impressive AI math display to date.
- The standout finding is a non-sofic group disproving the conjecture that all countable groups are sofic — a property first described in 1999 and previously thought to apply universally.
- Francesco Fournier-Facio at Cambridge, who has studied soficity since his 2020 PhD, said Astra's solution leans heavily on 2016 and 2019 papers by Andreas Thom and Gábor Kun, arguing AI 'couldn't have' reached the counterexample without prior human work.
- OpenAI initially claimed the 10 problems 'have seen no progress on the main result for at least a decade,' but revised that statement after Fournier-Facio contested it.
- Fournier-Facio warned that most AI math breakthroughs so far are counterexamples — fast and easy to verify — rather than new theory, where 'there's no tick at the end' to confirm a result.
- Elon Musk tweeted that the non-sofic group discovery is evidence the singularity has arrived.
- The release follows other recent AI math milestones: OpenAI cracking an Erdős conjecture in May and Claude Fable 5 disproving the century-old Jacobian conjecture last month.
Why it matters: A Cambridge mathematician who has studied soficity since his 2020 PhD says AI labs aren't being transparent about how their solutions rely on prior human work — and OpenAI already revised its claim that none of the 10 problems had seen progress in over a decade after being challenged. For mathematicians, the real test is whether AI can independently develop theory, not just find counterexamples that verify in minutes.
