OpenAI's Astra Solved 10 Open Math Problems — and the Price Tag Is the Real Story

Every once in a while an AI announcement lands that isn't about a chat UI or a new benchmark, but about the actual substance of what these systems can now do. OpenAI's announcement of ten new results in mathematics and theoretical computer science — produced by an internal version of Astra, their next major model — is one of those moments. Here's what happened, why it matters beyond the math community, and where the honest caveats are. The results The ten problems span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics. Highlights include: Non-sofic groups — a construction establishing their existence, addressing a central open question in group theory. Connes's rigidity conjecture — a disproof of a longstanding conjecture about von Neumann algebras. Quantum parallel repetition — an exponential parallel repetition theorem for general two-player quantum games. Multicolor Ramsey numbers — a superexponential lower bound, resolving Erdős problem 183. Closest vector problem — polynomial-factor hardness of approximation, a foundational lattice question tied to post-quantum cryptography. Each argument was prepared into a manuscript by humans working with the model, then formalized by the model into a Lean certificate (the proofs are public on GitHub). OpenAI also released the model's narration of its own thinking process for each solution. The price tag that reframes everything The most striking number in the announcement isn't the math — it's the cost. The total tokens needed to find these solutions would cost roughly $2,000 at Sol API rates . Think about that for a second. Two thousand dollars of compute to resolve open problems that mathematicians have worked on for decades. Some of these (like non-sofic groups) have been open for over a decade of intense effort. We're not talking about a moonshot lab budget — we're talking about the price of a mid