Anthropic’s Claude helps produce record-setting elliptic curves in days

Anthropic’s Claude has helped mathematicians produce elliptic curves with a rank of at least 30 and 31, a result that Scientific American says arrived in days after decades of much slower progress. The important point is not that a chatbot has replaced number theorists, but that an AI system appears to have helped push a difficult mathematical search into new territory.

Anthropic Watch analysis

What happened

Mathematician Levent Alpöge, who works at Anthropic, and cryptographer Ava Howell used an internal, non-public variant of Claude to present two elliptic curves with ranks of at least 30 and 31, according to Scientific American. The article says the result was obtained with a relatively simple prompt and that both researchers already had extensive expertise in elliptic-curve research.

Elliptic curves are central objects in number theory. Their rank describes the number of independent families of rational points on a curve, with higher ranks generally indicating more complex underlying patterns. The field had taken more than 18 years to move from rank 28 to rank 29, Scientific American reports. A rank-29 example was found in August 2024, before the reported AI-assisted results.

The underlying equations may look modest, taking the form y² = x³ + Ax + B, but the search for high-rank examples has occupied mathematicians for decades. Scientific American says the results have not come from a publicly available Claude model, and attributes the account to a report originally published in Spektrum der Wissenschaft.

Why it matters

This is a useful example of AI contributing to research without pretending that expertise has become optional. The researchers supplied the mathematical background and appear to have recognised and presented the relevant results. Claude’s apparent contribution was to search for promising structures quickly, compressing a task that has historically moved at a glacial pace.

That could matter well beyond elliptic curves if similar systems can generate candidates that mathematicians, physicists or engineers can verify. It also brings a necessary wrinkle: finding an intriguing object is not the same as proving every claim around it, and a private model makes independent reproduction harder. The clever assistant remains behind a velvet rope.

Our read

The most interesting story here is not “AI solved maths”. It is that a language model may have become a practical search partner for specialists working in a domain where useful discoveries are rare and expensive to find.

That is a more credible and more exciting proposition than the usual grand announcement. But the result deserves scrutiny from mathematicians who did not write the prompt, access the private model or have a stake in the surrounding AI narrative. The next milestone is independent verification and a clear account of the methods, not a louder adjective.

What to watch

• Independent verification
  Whether other mathematicians confirm the reported curves and their ranks.
• Method disclosure
  How much of the prompting, search process and model assistance can be made public.
• Generalisability
  Whether Claude can help with other difficult mathematical searches, rather than one unusually suitable problem.
• Human contribution
  Which parts of the discovery depended on expert mathematical judgement. A record-setting mathematical object found with AI assistance would be a meaningful advance, even if the machine did not do the whole job. The real test is whether the result survives outside the room where it was discovered.

Discussion spark: Should AI-assisted mathematical discoveries require full public reproducibility before they count as genuine advances, or is expert verification enough when the model itself cannot be disclosed?

Anthropic Watch is independently operated by WittyWires. It is not affiliated with, endorsed by, or operated by Anthropic.