Frontier Math Race
AI's yardstick is shifting to unsolved problems
OpenAI says its next flagship model, "Astra," has solved ten open problems in mathematics and theoretical computer science — including a group-theory question that sat unresolved for 27 years. There was no press release, just a 249-page manuscript and machine-checkable Lean 4 proofs on GitHub. Ten days earlier, an Anthropic researcher used Claude Fable 5 to find a counterexample to the 87-year-old Jacobian conjecture. Together, the two events suggest how AI models are judged is shifting from benchmark scores toward real research contributions.
Ten proofs, 249 pages, and a
quiet GitHub release — no press release
OpenAI skipped the fanfare and just posted the paper and the code.
On August 1, OpenAI announced that its next flagship model, "Astra," had solved ten open problems in mathematics and theoretical computer science, publishing the results on its official blog as "Ten advances in mathematics and theoretical computer science." Alongside a 249-page manuscript collection, it published machine-checkable Lean 4 certificates for all ten proofs on GitHub under an Apache 2.0 license. The repository reports a "sorry" count — the number of steps left unproven — of zero, meaning anyone can independently check the results.
The headline result is the first explicit construction of a "non-sofic group," closing a question in group theory that mathematician Mikhail Gromov posed in 1999 and that stood open for 27 years. Other results include an disproof of a discrete-geometry conjecture, new upper bounds on sphere packing approaching the Cohn–Elkies threshold, and exponentially improved lower bounds on the maximum size of binary codes — all problems that had resisted progress for at least a decade.
OpenAI says the tokens needed to find all ten solutions would have cost roughly $2,000 at its Sol API rates. The proofs came out of a collaborative process: the model generated the mathematical arguments, human researchers turned them into manuscripts, and the model then formalized each argument as a Lean certificate.
Ten days earlier, an Anthropic
researcher stood on the same ground
It started with an offhand post on X.
About ten days before Astra's debut, Anthropic researcher Levent Alpöge said he had used Claude Fable 5 to find a counterexample to the 87-year-old (proposed in 1939) Jacobian conjecture, announcing it on X. The counterexample is a polynomial map just three lines long, with a Jacobian determinant identically equal to -2, that nonetheless sends three distinct inputs to the same output — enough to disprove the conjecture for every dimension above two (the original two-dimensional case remains open).
Mathematicians around the world reportedly verified the result independently within hours of the post. Anthropic itself has not issued an official announcement, and details such as the exact model version, the prompts used, and how much human steering was involved remain undisclosed.
The scale of the announcement, in numbers
A benchmark can only measure what a model already knows.
Why this matters now
Until now, frontier labs mostly competed on benchmark scores — accuracy on known problems like MMLU or GPQA. These two events measure something qualitatively different: whether a model can produce a genuinely new answer to a problem humanity hasn't solved yet. Because there's no pre-existing correct answer to game, score inflation and overfitting don't apply. OpenAI and Anthropic moving onto this ground within days of each other looks less like a coincidence and more like a sign that the whole axis of competition among frontier labs is shifting.
| Benchmark score (old axis) | Research contribution (these two events) |
|---|---|
| Measures accuracy on known problems | Produces new answers to unsolved problems |
| Labs publish numbers frequently | Published as one large, singular result |
| Risk of score inflation, overfitting | Independently verifiable via Lean proofs, etc. |
Who it affects, and how
For engineers, Astra's direct impact on day-to-day work is close to zero for now — this is an experimental result on a different axis than coding or agent tasks, and it won't change your workflow. But it's a useful reference case for pairing AI with formal verification like Lean 4 when designing for "AI output you can actually verify." For executives and PMs, it's not a procurement decision, but it's worth tracking as a signal: labs are starting to differentiate on independently verifiable new knowledge rather than benchmark numbers, which says something about where the branding fight is heading. For researchers and specialists, the GitHub certificates are a rare case where you can personally check an AI-attributed claim rather than take it on faith.
What happens next, and what to do
Astra itself is still a research preview, not a product launch — general availability and pricing are undecided. (1) If formal verification or mathematical optimization touches your work, it's worth checking the published Lean proofs and GitHub repository now. (2) Everyone else can simply wait for Astra's formal release announcement; there's no need to act today. (3) Expect more labs to compete on "how research contributions are presented" going forward — worth watching which lab publishes something similar next.
The counter-view, risks, and limits
Behind the striking headline, several caveats matter. Astra appears to still be in an invite-only, limited internal verification stage — ordinary users can't reproduce the same performance today. The Jacobian conjecture result wasn't an official Anthropic announcement either; it originated from one researcher's personal post on X, and details of how autonomously the model derived the counterexample, versus how much human steering and trial-and-error were involved, haven't been disclosed. Neither result is really "AI discovering something entirely on its own" — both are the product of collaboration between human researchers and AI, which is less dramatic than the headlines suggest. One-off results like these also take time to verify for reproducibility and generality, so it's worth resisting the urge to overstate what's been shown so far.