OpenAI Says Its Unreleased "Astra" Model Produced Results on 10 Open Math Problems
OpenAI announced that an internal version of its unreleased model, Astra, produced results on 10 problems that have stayed open for years in mathematics and theoretical computer science. What sets the claim apart from the usual "benchmark score" news: each argument was formalized in a system called Lean so it can be machine-checked.
In brief
- What's claimed: the internal "Astra" model resolved or advanced 10 open problems spanning high-dimensional geometry, coding theory, group theory, operator algebras, quantum complexity, and lattice cryptography. Some are famous Erdős problems (183, 146, 180). It disproves one of Connes's conjectures and sets a new lower bound for multicolor Ramsey numbers.
- Verification: each argument was formalized in a Lean certificate — meaning the proof was machine-checked. That's far stronger evidence than a self-reported score; but whether the formal statement truly captures the problem, and the real assessment, is for the mathematical community to judge.
- The human part: humans prepared the manuscripts, but OpenAI is explicit: "the mathematical arguments themselves were generated by our system," and it takes responsibility for correctness. It adds that claiming human authorship for AI-generated proofs would be wrong.
- Scale: the tokens needed to find the solutions would cost roughly $2,000 at Sol API rates. OpenAI also shared an AI-generated disproof (of Erdős's unit-distance conjecture) back in May.
Our take
This is different from "a new model scored X on a test." Formalizing in Lean means the proof is machine-checked — so "did it actually solve it" rests on far firmer ground than a self-reported score. Even so, the real test is the community examining these results and placing them in context; OpenAI itself frames the news exactly that way. For our audience (professionals and SMBs trying to grow a business), there's no tool here you'll use tomorrow — this is frontier science, not everyday software. But the direction is striking: AI is moving from "an assistant that edits what a human wrote" toward "a system that produces original results at the edge of human knowledge," and doing it for a few thousand dollars of compute. It's a good signal of where things are heading; for a firm verdict, let's wait for the community's review.
Kaynak: OpenAI