Noesion Radarnoesion.ai
Research2026-07-30

Epoch AI published a problem from FrontierMath: Open Problems, its benchmark of unsolved research mathematics, asking for a genus 2 curve over the rationals whose Jacobian has a rational torsion point of prime order at least 31 — beyond the largest known prime torsion order of 29 found by Leprévost. In a pre-release test on July 30, 2026, GPT 5.6 Sol produced a solution that passed the problem verifier, and the problem is counted as solved on release. Sol did not derive a new curve: it located one by search in a public repository maintained by Edgar Costa and Timo Keller, meaning the answer was already latent in the literature and would have been recognized had someone checked the curve's torsion subgroup. Epoch AI is raising the target to a rational point of order 37, intended to sit beyond the current research frontier.

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