OpenAI's unreleased Astra AI model has solved 10 long-open problems in mathematics, publishing machine-checkable proofs for each. The breakthroughs, including disproving Connes’s rigidity conjecture, are seen as "big news" by experts, contrasting with a prior false claim by OpenAI in 2025. The results arrive amid growing concern in the math community over AI's role and lack of peer review.
Astra mathematical breakthroughs
- ▪Astra disproved Connes’s rigidity conjecture, posed in 1980, and proved Ehrhart’s volume conjecture
- ▪One major result is the construction of a non-sofic group, a problem open since Mikhail Gromov introduced the concept in 1999
- ▪An internal version of OpenAI's Astra model produced new results for 10 long-open problems in mathematics and theoretical computer science
- ▪The model also solved three problems from Paul Erdős’s catalog, including problem 183 on multicolor Ramsey numbers
Lean proof verification
- ▪The results have not yet been through peer review, and mathematicians must still verify that the formal statements match the problems
- ▪OpenAI published machine-checkable proofs for all 10 results, including a 249-page manuscript and Lean 4 certificates
- ▪The Lean 4 certificates are available on GitHub under an Apache 2.0 license and have a "sorry" count of zero, indicating no steps were left unproven
Previous GPT-5 controversy
- ▪In October 2025, OpenAI's then vice president of science, Kevin Weil, falsely claimed GPT-5 had solved 10 unsolved Erdős problems
- ▪Thomas Bloom described the new Astra results as "big news," rating them higher than a previous OpenAI counterexample he helped verify
- ▪Following the 2025 incident, Kevin Weil deleted his post, and Google DeepMind CEO Demis Hassabis called it embarrassing
- ▪Erdős problem database maintainer Thomas Bloom called the 2025 claim a "dramatic misrepresentation," as the model had only found existing papers
Computational cost efficiency
- ▪While the mathematical arguments came from Astra, human researchers turned the model's output into publishable papers
- ▪OpenAI estimated the total token cost for solving all 10 problems at approximately $2,000, based on GPT-5.6 Sol API rates
Mathematical community backlash
- ▪The Leiden Declaration warns that AI companies are "using published research without consent, bypassing peer review, and threatening the integrity of proof and attribution."
- ▪In June, the International Mathematical Union endorsed the Leiden Declaration, which criticizes AI companies' use of published research
- ▪Software engineer Fernando Borretti argued that AI will push the frontier of mathematics beyond human comprehension
Astra release timeline uncertainty
- ▪OpenAI research scientist Noam Brown called the results "a major step for scientific reasoning."
- ▪Astra is described as an unreleased model family designed to coordinate multiple agents for long tasks
- ▪OpenAI has not announced a release date, pricing, or final name for the Astra model family
- ▪Any launch of Astra must undergo the federal AI safety review process that previously delayed the GPT-5.6 rollout
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