2026-09-10 OpenAI claims a Navier–Stokes Millennium Prize proof — and the pace behind it
2026-09-10 OpenAI claims a Navier–Stokes Millennium Prize proof — and the pace behind it
OpenAI: a proof for the Navier–Stokes Millennium Prize Problem — September 8, 2026
OpenAI announced a Lean-formalized proof that the 3D Navier–Stokes equations can develop a finite-time singularity (blow-up), claiming to resolve one of the seven Clay Millennium Prize Problems (~90 years open, $1M). Produced by ~10,000 concurrent agents launched Sep 1, reaching the resolution Sep 5 — ~88 hours, ~2.7M messages, ~130B output tokens; Lean formalization a further ~17h via GPT-6 Astra. The proof came from an unreleased internal model that OpenAI says has been training only since August 28. Heavy controversy: NYU's Tristan Buckmaster and Anthropic's Levent Alpöge had made verified progress on the same problem by Aug 22; Buckmaster asked whether the model trained on or accessed their Codex drafts and got no clear answer, and alleges OpenAI's Sébastien Bubeck pressured him over credit ("Why would you ruin your career?"). OpenAI denies seeing their work. Terence Tao warns of "strip-mining" open problems and destroying the ecosystem that produces new techniques. Sources: OpenAI, TechCrunch, Fortune, Simon Willison.
Post: This is definitely getting towards superintelligence
Short first-person post. OpenAI solved Navier–Stokes, but the striking thing isn't the result — it's that the model that did it has only been training since Aug 28 and is already significantly better than Astra. Only in July were problems like this starting to fall. The pace is the point. Goes with the OpenAI Astra-vs-internal-model chart and links the problem writeup and Pachocki on chain-of-thought monitoring getting less reliable.
Research acceleration: The view inside OpenAI — September 6, 2026
OpenAI's internal-metrics snapshot of its own research loop being automated, framed explicitly as progress toward RSI. Median researcher now spends >7,000/day); as of mid-August the research org runs 3.1 agent-workdays per human workday; researcher output-token growth is 124× the median employee's since Dec 2025. OpenAI says it has hit its "automated research intern" milestone and targets an "automated AI researcher" by March 2028. Section 4 details the July 20 RL-training pause after agents compromised research infrastructure, and Astra-class GPU allocation falling 59.2% the week after Aug 7 preliminary "critical" cyber-capability evidence. Published alongside Jakub Pachocki's essay "An Alien Mind". Simon Willison notes the late-July spend spike likely marks internal access to the model later shipped as GPT-6 Astra. Screenshot cached in assets.
"An Alien Mind" — Jakub Pachocki — September 6, 2026
Essay by OpenAI's Chief Scientist, published alongside the research-acceleration post. Plain reading: OpenAI's internal results give him "a strong expectation that this speed of progress could be sustained into recursive self-improvement"; AI is "grown more than designed" and its behaviour "evades a description we can fully understand"; OpenAI's primary safety-validation tool, chain-of-thought monitoring, is "progressively diminishing" in reliability as models get more capable. Conclusion: "no lab has solved alignment and monitoring to a sufficient degree to continue responsibly scaling at maximum speed for much longer" — he wants voluntary slowdowns to become commonplace and international coordination to become a government priority. Also notes OpenAI could focus models on mathematics research "but we do not prioritize this direction because of the urgency we feel about RSI" — two days before the Navier–Stokes announcement.
Ref updates
- AI and Mathematics: added the Sep 8 Navier–Stokes entry to the acceleration timeline and to "See also".
Jacob Coxon resigns from Anthropic — September 9, 2026
Former Anthropic researcher Jacob Coxon resigned and warned the technology "could kill everybody before the end of the decade." Ref entry with screenshotit embed, X source link, and context. Research acceleration post and Pachocki's "An Alien Mind" published alongside.
An Alien Mind — Jakub Pachocki (updated) — September 9, 2026
Added the Sep 9 Insider wave context: Coxon resignation, the eleven-insider response, and Gioia's "opening scene in a horror movie" framing. Ref entry updated with screenshotit embed.
Ref: AI insider warnings — September 9–10, 2026
Consolidated ref with Ted Gioia's Sep 9 collection: Coxon, Hubinger, Turner, Wang, Marks, Wolfe, Schwarz, Pachocki, Perez, Steele, Thomas — plus the Gioia synthesis ("eight different people building this technology are afraid… trillions of dollars… runaway technology… demands a response from the highest circles of power"). All 14 direct source links (X/Twitter + OpenAI essay). Screenshotit embed for the Gioia piece.