OpenAI said on August 1 that an internal, unreleased model called Astra produced solutions to ten problems in mathematics and theoretical computer science that had resisted progress for at least a decade, several for much longer, publishing machine-checked proofs alongside the claims.

The announcement came weeks after OpenAI cut prices across its current GPT-5.6 lineup, including an 80% cut to its Luna tier. OpenAI described Astra as its “next major model family,” built for long, multi-step problem solving rather than quick chat replies. Astra itself has not shipped, and OpenAI has not said whether it will launch as GPT-6, a GPT-5.7 update, or under a different name.

Ten long-standing problems

The results span group theory, high-dimensional geometry, coding theory, quantum complexity, lattice cryptography and extremal combinatorics, according to OpenAI. The most notable is the first explicit construction of a non-sofic group, closing a question in group theory open since mathematician Mikhail Gromov defined sofic groups in 1999. Astra also produced a disproof of Connes’s rigidity conjecture on von Neumann algebras, a proof of Ehrhart’s volume conjecture, the first improvement to a general high-dimensional sphere-packing bound since 1978, and solutions to three problems from mathematician Paul Erdős’s long-standing list of open questions.

None of the results touch the seven Millennium Prize Problems. OpenAI put the total compute cost of generating all ten solutions at roughly $2,000 at its Sol API pricing — a figure researchers have pointed to as remarkably low for results of this kind.

Machine-checked, not yet peer-reviewed

Rather than asking readers to take the arguments on faith, OpenAI said it formalized each proof as a Lean certificate — a format a separate program can check line by line for logical validity — and published a 249-page manuscript alongside the certificates. That is a higher verification bar than OpenAI’s earlier claim that GPT-5.6 Sol Ultra had proved a 50-year-old graph theory conjecture, which mathematicians said would take weeks to fully check.

A machine-checked certificate confirms a proof is logically sound; it does not by itself establish how the wider mathematical community will judge the results’ significance, and independent commentary beyond OpenAI’s own account had not surfaced by publication time. For more on how these checks work, see our explainer on how AI math proofs are verified.

OpenAI added that Astra will be the first model it submits to the US government’s new pre-release safety review before any public launch.

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