Claude and two mathematicians found a rank 31 elliptic curve

A record in pure mathematics that had improved once in eighteen years improved twice in three days, with an AI model credited alongside the two mathematicians who ran the search.

Epoch AI has marked its FrontierMath elliptic curve rank problem “Solved (AI)”. That label is the newsworthy part: this is not a model reproducing a known answer on a benchmark, it is a mathematical object that number theorists had hunted for decades, now exhibited and open to verification by anyone.

What the problem asked for

The open problem required an elliptic curve over the rationals with rank at least 30, together with 30 explicitly exhibited, linearly independent rational points. Exhibiting the points is what makes the claim checkable rather than asserted.

The standing record was rank 29, set by Noam Elkies and Zev Klagsbrun in 2024. That result had itself been the first improvement in eighteen years, which is the measure of how slowly this particular number moves.

What was found, and when

A rank 30 curve appeared on the Elliptic Curve Rank Leaderboard on August 20, 2026, credited to Claude working with mathematicians Levent Alpoge and Ava Howell. The same team posted a rank 31 curve on August 23.

Assuming two standard conjectures, Birch and Swinnerton-Dyer and the Generalized Riemann Hypothesis, the curves have rank exactly 30 and 31 rather than merely at least that.

Whether this becomes a pattern

The result did not arrive alone. Earlier in August, OpenAI’s Sol model produced a proof of the Crouzeix conjecture, a separate long-open problem at a different laboratory.

Two labs closing two different kinds of open problem within weeks of each other is either coincidence or the beginning of a cadence, and one month of evidence cannot distinguish between them. The measurable test is whether results of this kind keep appearing on public leaderboards where the work can be checked, rather than in company announcements where it cannot.