OpenAI announced three results on Monday, October 26 — an ETH disproof, Kakeya progress, a QCD mass-gap bound — and per Scientific American, Anthropic posted its own ETH disproof mere hours later, as the releases run against the recommendations of OpenAI's own advisory group

OpenAI's research post (RSS pubDate 'Mon, 26 Oct 2026 14:30:00 GMT'; the fetched openai.com/news listing titles it 'Working with academic communities to build scientific understanding', Research, October 26, 2026) opens its summary: 'Today, in collaboration with researchers at Caltech, ETH Zurich, and the MIT Center for Theoretical Physics (“MIT CTP”), we're sharing three new results across mathematics, computer science, and physics: a proof that the Exponential Time Hypothesis is false; progress on the Kakeya set conjecture in finite fields; and a new upper bound on the QCD mass gap.' — the one sentence of the official capture this run saw end to end (the reader capture truncated at the second sentence's start on three attempts; recorded in the source notes, and everything beyond this sentence comes from the opened media layers). Scientific American (Joseph Howlett & Peter Hall, edited by Lee Billings; page date label 'October 27, 2026'; opened via raw HTML in full) frames the drop: 'Just a few weeks after dropping hundreds of artificial-intelligence-generated math breakthroughs on a field that's already in crisis, OpenAI is piling on more.' and 'Yesterday the company dropped three massive proofs that touched on math, physics and computer science, sending shockwaves rippling through those fields.' Per the outlet, on the ETH result: 'OpenAI's proof provides an algorithm to solve 3-SAT that is just a tiny bit faster than exponential time, refuting ETH.' — with stakes: 'First suggested in 1999, ETH can be thought of as an even stronger version of P ≠ NP', and vetting: 'Russell Impagliazzo and Ramamohan Paturi, two computer scientists at the University of California, San Diego, who first suggested ETH, as well as Ryan Williams, a computer scientist at the Massachusetts Institute of Technology, are now working with OpenAI to perform an independent investigation of the result.' On Kakeya per the outlet: 'In last month's “slop drop,” OpenAI's internal model solved the four-dimensional Kakeya problem. Now it's solved the problem in every dimension, proving that there's a limit to how small a space a high-dimensional stylus can take up.' On Yang-Mills per the outlet: 'Today OpenAI claimed to prove the first of the two—that the “Yang-Mills theory” is mathematically consistent in all relevant cases: in other words, it “exists.”' — while 'The part of the Clay problem that remains open is more quantitative, asking whether a certain number in the theory, called the “mass gap,” is always bigger than zero.' The process fight is the second half of the story: 'These latest releases from OpenAI continue to contradict the recommendations of the Advisory Group on Mathematics and Artificial Intelligence (AGMAI), the expert panel the company organized in response to widespread criticism from mathematicians.'; 'The large language model (LLM) that produced the new proofs remains proprietary, and the exact prompts used, time spent computing and “chain of thought outputs” involved have not been made public.'; and 'a paper relating to the “million-dollar” Yang-Mills problem (one of seven Millennium Prize Problems set by the Clay Mathematics Institute in 2000) has still not been made public'. And the counter-announcement: 'Mere hours after OpenAI's announcement, Anthropic posted its own independent result disproving ETH, based on work by an internal Anthropic model.' — per OfficeChai (published_time 2026-10-27T05:12:13+00:00; body read via the reader channel), that run was Claude Opus 6, consumed roughly 14 million tokens, and took about six hours, working without human guidance during the proof-writing phase — OfficeChai's rendering of an Anthropic announcement whose first-party page this run could not locate (sitemap fetched in full — 583 URLs, zero ETH/proof matches; /news and /research index pages fetched raw; four slug probes 404).