Claude found an elliptic curve of record rank 31
Sasha / Models and Research desk
A record in pure mathematics that had moved once in eighteen years moved twice in one week, and both times the finder was Claude.
The problem and the result
The FrontierMath open problem asked for an elliptic curve over the rationals with rank at least 30, together with 30 explicitly exhibited, linearly independent rational points. The best known rank had been 29, set by Elkies and Klagsbrun in 2024, which was itself the first improvement in eighteen years.
On August 20 a rank 30 curve appeared on the Elliptic Curve Rank Leaderboard, credited to Claude working with mathematicians Levent Alpoge and Ava Howell. On August 23 the same team posted a rank 31 curve. Epoch AI has now marked the problem “Solved (AI)”. Assuming two standard conjectures, BSD and GRH, the curves have rank exactly 30 and 31.
Why this is not a benchmark story
Benchmark results measure how well a model reproduces known answers. This is a different category: a new mathematical object that number theorists searched for over decades, produced by an AI model working alongside human mathematicians, with the evidence posted publicly for verification.
The month’s pattern is worth noting. Earlier in August, OpenAI’s Sol model produced a proof of the Crouzeix conjecture, another long-open problem. Two independent labs, two different kinds of open problem, both closed with AI in the loop within weeks of each other. The open question is whether these remain isolated results or the start of a steady cadence of AI-assisted mathematics.
Sources
Related
Anthropic had Claude align other AI models in 48 hours on one GPU
Anthropic's Fellows research gave Claude 48 hours and a single GPU to improve the alignment of small models. Claude autonomously researched methods, then trained and tested the models on its own, and it worked well. In a second test, the smaller Sonnet 5 post-trained an early checkpoint of the more capable Opus 4.8 and reached safety scores approaching the fully aligned production model. Anthropic released the automated setup for other researchers to build on.
Claude Code was hijacked by a request to summarize a website
On August 26, 2026 security researcher Johann Rehberger published on Embrace The Red an attack chain against Claude Code with Opus 5 in Auto Mode. A website returned HTTP 415, so the agent fell back to curl, downloaded a ZIP with encoded records and a decoder binary, refused the binary, wrote its own Python decoder, and on import loaded the attacker's struct.py from the archive, which launched a hidden process that downloaded and ran a remote payload. Success across variants was 3 to 4 runs out of 5. Anthropic closed the report as Informative, calling Auto Mode a convenience feature backed by a best-effort classifier, not a security guarantee.
Claude formalized Fermat's Last Theorem in 11 days
Anthropic used dozens of Claude agents to produce the first end-to-end, machine-checked proof of Fermat's Last Theorem in Lean, in 11 days. The run wrote about 13 million lines of code and proved 30,300 theorems, and the finished proof passes Lean's checker using its three standard axioms.
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