OpenAI's unreleased Astra model just cracked 10 long-standing math problems

For a long time, the prevailing wisdom was that AI could only remix existing human knowledge, not chart new frontiers in pure mathematics. That assumption just hit a massive wall.

OpenAI revealed that an internal version of its next major model, codenamed Astra, solved or made substantial progress on 10 open problems across mathematics and theoretical computer science. None of these problems had moved in at least a decade, with some evading researchers for nearly thirty years.

Even more staggering is the price tag. OpenAI estimated that all the tokens required to discover the solutions across all 10 problems would cost roughly $2,000 at Sol API rates.

Cracking Connes and Erdős with Lean verification

These were not trivial classroom exercises. The breakthroughs span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics.

Among the highlights, Astra settled a central question in group theory by constructing non-sofic groups, an elusive symmetry structure that mathematicians have hunted since 1999. It also disproved Alain Connes's longstanding rigidity conjecture, resolved Ehrhart's volume conjecture across dimensions, and cleared out three separate Erdős problems (numbers 146, 180, and 183).

In cryptography, Astra established polynomial-factor hardness of approximation for the closest vector problem (CVP), a cornerstone of lattice-based post-quantum cryptography. It also tightened theoretical upper bounds in high-dimensional sphere packing down to the Cohn-Elkies threshold.

Every mathematical argument was generated by Astra, turned into manuscripts alongside human collaborators, and formally verified in computer-checked Lean certificates. OpenAI also published the model's full reasoning chain traces for each solution.

The research world moved just as fast. Within 24 hours, Anthropic's Levent Alpoge claimed he was able to reproduce five of the ten proofs using Anthropic's Fable model on a generic prompt with zero internet access.

The authorship debate

When a model does the heavy lifting, who gets the credit? OpenAI directly addressed the tension, referencing concerns from mathematicians including signers of the Leiden declaration on AI and Mathematics.

OpenAI stated that human authorship should not be claimed for proofs generated entirely by AI, as that would misrepresent both machine capability and genuine human effort. The company took responsibility for correctness and formalization in Lean, but credited the mathematical arguments to Astra.

Naturally, that immediately sparked debate across forums: can an AI system's output be considered Fields Medal-worthy when the machine did the actual thinking?

Why it matters

In our view, the most radical detail in this announcement isn't just the math; it's the $2,000.

For years, frontier AI research felt like an exclusive sport for tech giants burning millions on brute-force search. But if resolving 10 decade-old mathematical roadblocks costs only a couple thousand dollars in API tokens, deep research suddenly becomes accessible to individual mathematicians and small academic departments. We think this fundamentally shifts how theoretical science will be funded and explored.

Competitively, the fact that Anthropic's Fable reproduced five proofs within a single day shows that the gap between frontier reasoning architectures is razor-thin. Everyone is converging on the same playbook: high-reasoning models coupled with automated formal proof engines like Lean to eliminate hallucinations.

Mathematicians no longer have to spend years verifying sketchy manuscripts manually. The machine drafts the logic, Lean verifies it, and humans focus on posing the right questions. As this loop moves beyond pure math into biology and materials science, the speed of actual discovery is about to look very different.