The AI takeover of mathematics has begun
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- OpenAI announced its unreleased model "Astra" solved 10 long-standing mathematics problems spanning sphere packing, error-correcting codes, non-sofic groups, and quantum game theory, releasing 250+ pages of papers verified with Lean software
- OpenAI revised its announcement language after Gábor Kun of the Alfréd Rényi Institute objected that the original framing — claiming the problems had seen "no progress" for decades — minimized contributions by Kun and Andreas Thom, calling it "rather sloppy"
- Mathematicians told The Verge the problems were the kind of breakthroughs that would normally secure an academic position, with Yang-Hui He saying many felt a "phase transition" over the past six months in AI's mathematical capability
- OpenAI estimated the 10 solutions cost roughly $2,000 in tokens at current API prices, though researchers said the true cost was likely considerably higher accounting for failed attempts
- Oxford Fields Medalist James Maynard said he has spent the past year "soul searching," describing palpable excitement alongside "despair" about what AI advancement means for future mathematicians
- In May, OpenAI cracked an Erdős conjecture open for nearly a century; in July, Harvard's Levent Alpöge reported Anthropic's Claude Fable 5 disproved the Jacobian conjecture with a tiny counterexample
- Researchers including Colva Roney-Dougal warned proprietary AI access could lock out less-wealthy institutions, since mathematics traditionally operates on shoestring budgets with open-source tools unlike the tightly controlled models from OpenAI and Anthropic
Why it matters: Mathematics has long operated cheaply and openly, but proprietary AI models like Astra — whose true compute costs exceed the $2,000 OpenAI advertised — risk creating a paywall-driven research divide that disadvantages smaller institutions and accelerates commercial intrusion into a field that has historically resisted it.
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