Documentary pack on the Navier–Stokes announcement

UE Recherche, Introduction to Epistemology, IMT Atlantique

This pack gathers the sources available on OpenAI's announcement concerning the Navier–Stokes equations: PDF documents (the paper claiming the result, the official problem statement, a personal testimony) and web links where no PDF was available (institutional site, code repository, magazine article, blog post, video). Each source is labelled with its origin below.

It does not rank the sources or take a position on the announcement. Working through them should let you draw out, on your own, notions useful for judging such a claim.

PDF documents

  1. Existence and Smoothness of the Navier–Stokes Equation · official document Charles L. Fefferman (Princeton): the official statement of the Millennium Prize problem, as written for the Clay Mathematics Institute. 6 pages. navierstokes.pdf
  2. Finite Time Blowup for Navier–Stokes · preprint OpenAI: the full paper (166 pages) presenting the mathematical construction claimed by the 8 September 2026 announcement. navier-stokes.pdf
  3. Public statement by Tristan Buckmaster · testimony Tristan Buckmaster (New York University): a first-person account of his exchanges with OpenAI, published on his professional website (cims.nyu.edu). 4 pages. statement.pdf

Web links

  1. Clay Mathematics Institute news · institution Notice published by the institution that administers the Millennium Prize, about the announcement. claymath.org/news/navier-stokes-announcement
  2. On the Navier–Stokes Millennium Prize Problem · company blog Official OpenAI post presenting the result and the terms of its release. openai.com/index/navier-stokes-solution
  3. NavierStokesAndEuler repository · code repository OpenAI's GitHub repository containing the Lean formalization made public. github.com/openai/NavierStokesAndEuler
  4. Theorem Proving in Lean 4: Introduction · documentation Official documentation of the Lean language and proof assistant, useful for understanding what a formal verification guarantees. lean-lang.org/theorem_proving_in_lean4/Introduction
  5. AI Has Solved One of Math's $1 Million Millennium Prize Problems · science magazine Quanta Magazine: coverage of the announcement, with reactions from mathematicians in the field. quantamagazine.org
  6. If math is more than proof, we need to better celebrate the rest of it · guest post Grant Sanderson (3Blue1Brown): a guest post on Terence Tao's blog, reflecting on the place of proof in mathematical activity, published after the announcement. terrytao.wordpress.com
  7. Mathematicians learn little from AI completing unsolved problem · public radio NPR: coverage of how the mathematical community received the announcement, two weeks after it was published. npr.org