OpenAI Says Unreleased Astra Model Solved Ten Decades-Old Math Problems for $2,000
Does OpenAI's Astra math breakthrough represent genuine scientific progress worth the attention it's getting? OpenAI announced on August 1 that an internal, not-yet-released version of its next model family, called Astra, produced verified solutions to ten mathematics and theoretical computer science problems that had gone unsolved for at least a decade, some for nearly 30 years. The company published a 249-page manuscript alongside machine-checkable Lean 4 proof certificates for every result on GitHub, putting the total compute cost at roughly $2,000. The headline result is the first explicit construction of a non-sofic group, resolving a question in group theory that had stood open since mathematician Mikhail Gromov defined the concept in 1999.
Other results include a disproof of Connes's rigidity conjecture on von Neumann algebras, a proof of Ehrhart's volume conjecture, and solutions to three problems from Paul Erdos's catalogue, including problem 183 on multicolor Ramsey numbers. OpenAI's head of mathematics research, Sebastien Bubeck, called the results "beautiful" on X, and research scientist Noam Brown described them as a major step for scientific reasoning. Thomas Bloom, who runs the erdosproblems.com database at the University of Manchester, said the results were bigger news than an earlier unit-distance counterexample an OpenAI model produced in May.
Astra itself has not been released publicly, and OpenAI credits the model with the underlying mathematical reasoning while human researchers turned its output into publishable papers. The announcement lands months after mathematicians behind the Leiden Declaration, endorsed by the International Mathematical Union, warned that AI companies were using published research without consent and bypassing peer review.
What supporters say:
The results shipped with machine-checkable Lean proofs for every claim, letting anyone verify correctness instantly rather than waiting on traditional peer review.
Supporters see this as evidence AI can now generate original, verifiable contributions to frontier science rather than just optimizing known benchmarks, with implications for fields like drug discovery and materials science.
What critics say:
Independent replication of how Astra actually reached its answers is difficult right now since the model itself hasn't been released and OpenAI alone chose which problems to attempt.
Mathematicians behind the Leiden Declaration have accused AI companies of building on published research without consent and sidestepping peer review, a concern that colors reaction to Astra's results.
Some in the field note the ten problems, while genuine, weren't the discipline's biggest open questions like the Millennium Prize problems, raising questions about whether OpenAI selected winnable problems for a splashy announcement.
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