OpenAI's math papers: real progress on Riemann Hypothesis, pi's irrationality exponent pinned at 2
tdhopper · x · 2026-10-08
Mathematician John Cook reviews a batch of new mathematical papers from OpenAI, highlighting three results: the discrete Fourier transform can theoretically be computed slightly faster than O(n log n) (no practical impact yet, but possibly a path to more); π's irrationality exponent is 2, so don't expect exceptionally good rational approximations; and there's substantial progress toward the Riemann Hypothesis, enough to greatly tighten the provable error bound in the Prime Number Theorem. He also published side posts connecting Nathaniel Bowditch to Lissajous curves and a topological model for provability logic.
Related event: OpenAI Open-Sources 722 AI-Generated Math Manuscripts, Sparking Debate(254 posts)→
More from AGI Musings
- 'Corporations are superintelligence' takes get mercilessly mocked — tszzl · 2026-10-08
- Beff Jezos: Physics and math academia became decelerated, only acceleration is the way out — beffjezos · 2026-10-08
- AGI needn't be superhuman: matching an average human on most skills should count — fkasummer · 2026-10-08
- A week inside China's AI scene: why Doubao keeps its flagship closed at 300M users — Shot-Height-7194 · 2026-10-08
- LinkedIn users are retroactively adding 'AI' and scrubbing 'DEI' and 'remote work' from old job listings — sebkrier · 2026-10-08
- LessWrong Thought Experiment: How Should a Model Guess Today's Date With No Date Context? — LessWrong 精选 · 2026-10-08