OpenAI's Astra Model Solves Ten Decade-Old Mathematical Problems

On August 1, 2026, OpenAI announced that an internal version of its next major model, Astra, produced new results on ten mathematical problems that had been open for at least a decade, spanning geometry, coding theory, group theory, and quantum complexity [1]. OpenAI reports the total compute cost for all ten solutions was approximately $2,000 at Sol API rates, and has published Lean 4 formalizations in a public GitHub repository [1][2]. Alongside the mathematical results, OpenAI staked out an explicit normative position: that claiming human authorship for AI-generated proofs misrepresents both the AI's contribution and the nature of human intellectual work [1].

If the results hold to independent scrutiny, they show AI moving from a tool that assists mathematical work to one that independently advances it on problems humans had not solved for decades. The attribution argument OpenAI is making, if it gains traction in academic publishing, would require a substantial revision of how research credit is assigned when AI produces the core intellectual output.

On August 1, 2026, OpenAI published what it describes as ten advances in mathematics and theoretical computer science, produced by an internal version of its next major model, Astra [1]. The problems span geometry, coding theory, group theory, and quantum complexity, and each had seen no main-result progress for at least a decade — in most cases significantly longer. After Astra found solutions, human collaborators helped prepare manuscripts, and the same model then formalized each proof as a Lean 4 certificate, with all formalizations made publicly available in the openai/ten-proofs GitHub repository [2]. The company reports the total compute cost for all ten solutions would be roughly $2,000 at its Sol API token prices [1].

The announcement combines capability demonstration with normative intervention. OpenAI explicitly addressed the ongoing academic debate over AI attribution, arguing that crediting a human author for a proof generated by AI would misrepresent the AI's contribution and distort what counts as human intellectual work [1]. This position directly engages — and disagrees with — signatories of the Leiden declaration, who have argued for conservative attribution practices. OpenAI also notes that an earlier AI result, the disproof of the Erdős unit-distance conjecture, has already generated multiple subsequent published results by human researchers, framing AI output as productive rather than terminal for the field [1].

The reception within mathematics has been pronounced. Simon Willison described widespread reaction as a 'Deep Blue moment' — the existential reflection chess professionals experienced after Kasparov's 1997 loss — with some mathematicians reporting crisis about the discipline's future [2]. Terence Tao has offered a different framing: he envisions large-scale human-machine collaborations, where humans direct the creative components of mathematical work and AI handles technical execution, a model he calls 'big mathematics' [2].

The main methodological skepticism concerns the cost figure. While $2,000 for ten proofs sounds low, OpenAI disclosed no data on how many problems Astra attempted without reaching a solution, making the true efficiency of the approach difficult to evaluate independently [2]. The prompts used were also not published, which limits replication of the methodology.