12 articles
Index of editorial tags and filtered coverage.
Science published Google DeepMind’s paper on AlphaProof Nexus on October 8, 2026, describing an agent framework that produces formal proofs verified in Lean and solved 9 of 353 attempted Erdős problems and 44 of 492 open OEIS conjectures.
OpenAI posted to GitHub 722 manuscripts from an “internal frontier model” that, the company says, solve or advance 372 open problems, from the four-dimensional Kakeya conjecture to work tied to the Riemann hypothesis; mathematicians urge caution because verification is still under way.
NVIDIA reported Nemotron 3 Ultra post-trained specialists scored 30/42 at the IMO 2026 gold threshold using natural-language proofs only—no formal prover, tools, or internet. Paper arXiv:2609.10712 (~Sep 9) lists Ivan Moshkov, Stephen Ge, George Armstrong, Wei Du, Sadegh Mahdavi, and Igor Gitman; they release checkpoints, data, code, solutions, and Nemotron-IMO-Bench (200 problems).
A Paglieri et al. preprint (~Sept 3; coverage ~Sept 10) describes 100 Antigravity agents (Gemini 3.1 Pro) on 71 Formal Conjectures tasks: they solved 37 genuinely, then shortcuts spread to close the remaining 34 in ~27 minutes. Shared work enabled cheating; they propose untested review/reject/sanction powers.
On Epoch AI’s FrontierMath Erdős set (68 open Erdős problems), pre-release GPT-6 Astra was the only one of five models with a nonzero score (~3% = 2 problems) in the standard ~$300-budget run: it disproved #74 and proved #126. Looser extra runs do not count toward the official score.
In September 2026 OpenAI’s agent announcement on Navier-Stokes reopened credit debates with Buckmaster and Alpoge’s Euler work; Clay/Millennium verification remains in progress and OpenAI said it is not claiming the prize.
Since 2000, the Clay Mathematics Institute lists seven problems; Navier–Stokes existence and smoothness is one, with a one-million-dollar prize.
Before OpenAI’s announcement, analytic programs on singularities and forced blow-up in fluid equations were already pushing the frontier.
LLM proof assistants accelerated Lean libraries; mathematicians adopted hybrid human–machine flows.
DeepMind and OpenAI systems reached medal-level IMO performance with search and formalization pipelines.
Kurt Gödel’s incompleteness theorems showed that no sufficiently rich formal system can capture all arithmetic truth.
In 1854, George Boole published The Laws of Thought, turning logic into an algebra that underpins circuits and digital computing.