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Claude reportedly helps find an elliptic curve with rank of at least 31

Scientific American reports that Levent Alpöge and Ava Howell used an internal Claude variant to present two high-rank elliptic curves within days.

Updated Sep 16, 2026 · 12:56 UTC1 reports

The short version

  • Scientific American reports that mathematician Levent Alpöge and cryptographer Ava Howell used Claude to present elliptic curves with ranks of at least 30 and at least 31.[Scientific American]
  • The work took only a few days, according to the report; earlier progress from rank 28 to rank 29 took more than 18 years.[Scientific American]
  • The researchers used a Claude variant that is not publicly available. The reported ranks are lower bounds, not exact values.[Scientific American]

Key facts

  • Scientific American reports that Alpöge and Howell used Claude to present elliptic curves with ranks of at least 30 and at least 31 within a few days.[Scientific American]
  • The report says earlier progress from rank 28 to rank 29 took more than 18 years.[Scientific American]
  • The Claude variant used by the researchers is internal and unavailable to the public, according to Scientific American.[Scientific American]

What remains uncertain

  • The reporting gives lower bounds of 30 and 31 for the curves’ ranks, not exact values.[Scientific American]

Sources

Outlet counts describe coverage, not independent confirmation. Reports may share a wire service or original source.