OpenAI's Quasi-Riemann proof sparks chain of results, Bhargava proves primitive root theorem
Singularitarian · x · 2026-10-15
OpenAI's October 6 public proof of the Quasi-Riemann Hypothesis is cascading through number theory:
- A Hexagon preprint by Cureton and Thorner (Oct 12) shows all finite-order Hecke L-functions are zero-free to the right of 1 − 1/6000.
- Frei, Somos and Widmer then used this to unconditionally prove the 2007 Ellenberg–Venkatesh bounds on ℓ-torsion in class groups.
- Fields medalist Manjul Bhargava proved that every nonsquare integer not equal to −1 is a primitive root for a positive proportion of primes, with lower bound ca/(N log N), leveraging OpenAI's Type II estimates.
Amusing footnote: the second paper declares "No artificial intelligence tools were used in this work."
Related event: OpenAI's Quasi-Riemann Proof Sparks Chain of Number Theory Papers(2 posts)→
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