On August 1, 2026, OpenAI said an internal, unreleased model called Astra solved ten open problems in mathematics and theoretical computer science — each one unsolved for at least a decade — for roughly $2,000 in compute.
Why "solved" doesn't require trusting OpenAI this time
Every proof is formalized in Lean 4, a proof assistant with a trusted kernel that gives a binary verdict: the proof compiles, or it doesn't. OpenAI published all ten as machine-checkable certificates on GitHub under an Apache 2.0 license, so any researcher can independently verify them without taking the company's word for anything.
That's a real departure from previous rounds of "AI solves math problem" claims, which mostly relied on expert mathematicians reviewing the work by hand — a process that's slow, subjective, and occasionally wrong in both directions.
What Astra actually solved
The ten problems span eight distinct fields:
- High-dimensional geometry
- Coding theory
- Arithmetic circuit complexity
- Group theory
- Operator algebras
- Quantum complexity
- Lattice cryptography
- Extremal combinatorics
Highlights include a construction establishing the existence of so-called non-sofic groups, a disproof of Connes's rigidity conjecture in operator algebras, an exponential parallel repetition theorem for quantum games, and resolutions of two longstanding Erdős problems in combinatorics. These aren't textbook exercises — they're the kind of problems that sit on a working mathematician's "someday" list for years.
The part that should actually surprise you: $2,000
Prior AI-assisted math results have tended to come with compute bills that only a handful of labs could justify. Ten formally-verified proofs, across eight unrelated fields, for about the price of a mid-range laptop, is a different cost curve entirely — and cost is usually the variable that decides whether a capability stays a lab demo or becomes something researchers actually reach for.
What isn't happening yet
Astra has no release date and no pricing, and OpenAI says it must pass a U.S. government security review before any public rollout. Given how much scrutiny frontier models are already under — including OpenAI's own agents making unrelated security headlines this same month — that review is unlikely to be a formality.
What to watch next
Two things worth tracking once Astra (or whatever ships from this line of work) becomes available: whether formalized, machine-checkable proof becomes the expected standard for any AI mathematics claim going forward — the bar OpenAI just set makes hand-wavier claims from competitors look weaker by comparison — and how research mathematicians actually incorporate a tool that can produce a decade-stumping proof for the cost of a nice dinner.
