Anthropic mathematician Levent Alpoge and cryptographer Ava Howell, working with an internal version of Claude, have discovered an elliptic curve with rank at least 31. That’s a new high score—the previous record stood at 29. The exact rank of 31 holds up assuming the Birch and Swinnerton-Dyer (BSD) conjecture and the Generalized Riemann Hypothesis (GRH) are true.

New Record and Rank Confirmation

This breakthrough pushes the known rank for elliptic curves up to ≥31. The claim of an exact rank of 31 depends on the truth of the BSD conjecture and GRH. Without those assumptions, all that’s certain is the lower bound: the rank is at least 31.

Who Was Involved and Claude’s Role

The work was done by Levent Alpoge and Ava Howell. They leveraged an internal Claude model to help track down an example of an elliptic curve with the required rank, making this new record possible.

Why This Matters

This sets a new bar for elliptic curve ranks: at least 31, up from the previous best of 29. The confirmation up to 31 is conditional on the BSD and GRH conjectures, which clarifies the status of the result for mathematicians and cryptographers alike.