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NavierStokesAndEuler
Lean2026–2026
openai / NavierStokesAndEuler

NavierStokesAndEuler

Lean certificates accompanying Navier-Stokes and Euler results

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15Distinct people
20Mentions
0Explicit recommenders
2.1KGitHub stars
REPOSITORY AT A GLANCE

What to know before exploring

What it is

Lean certificates accompanying Navier-Stokes and Euler results

GitHub

Where it is used

The last source check was inconclusive. This does not establish whether a product uses it.

What people are saying

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No classified warning is attached to this page. Read the discussions before treating silence as approval.

Also in these discussions

No other repository is repeatedly linked in the same discussions.

This week on Hacker News

Nov 7–Nov 14 UTC · Direct repository links and separately labeled related project stories. Indexed through 11/14/2026, 5:04:57 PM UTC.

No direct repository links were found in the indexed HN discussions over the past seven days. Older discussions are available below.

Mentions over time

HN mentions by day20 dated mentions

Observed mentions: 2026-09-08 17:19:07 UTC to 2026-10-08 09:25:15 UTC.

02462026-09-08 00:00:00 UTC to 2026-09-09 00:00:00 UTC (exclusive): 4 mentions; 0 submissions, 4 commentsSep 82026-09-09 00:00:00 UTC to 2026-09-10 00:00:00 UTC (exclusive): 7 mentions; 1 submissions, 6 comments2026-09-10 00:00:00 UTC to 2026-09-11 00:00:00 UTC (exclusive): 1 mentions; 0 submissions, 1 comments2026-09-11 00:00:00 UTC to 2026-09-12 00:00:00 UTC (exclusive): 3 mentions; 1 submissions, 2 comments2026-09-12 00:00:00 UTC to 2026-09-13 00:00:00 UTC (exclusive): 1 mentions; 0 submissions, 1 comments2026-09-13 00:00:00 UTC to 2026-09-14 00:00:00 UTC (exclusive): 1 mentions; 0 submissions, 1 comments2026-09-14 00:00:00 UTC to 2026-09-15 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-15 00:00:00 UTC to 2026-09-16 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-16 00:00:00 UTC to 2026-09-17 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-17 00:00:00 UTC to 2026-09-18 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-18 00:00:00 UTC to 2026-09-19 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-19 00:00:00 UTC to 2026-09-20 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-20 00:00:00 UTC to 2026-09-21 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-21 00:00:00 UTC to 2026-09-22 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-22 00:00:00 UTC to 2026-09-23 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-23 00:00:00 UTC to 2026-09-24 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 commentsSep 232026-09-24 00:00:00 UTC to 2026-09-25 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-25 00:00:00 UTC to 2026-09-26 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-26 00:00:00 UTC to 2026-09-27 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-27 00:00:00 UTC to 2026-09-28 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-28 00:00:00 UTC to 2026-09-29 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-29 00:00:00 UTC to 2026-09-30 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-09-30 00:00:00 UTC to 2026-10-01 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-10-01 00:00:00 UTC to 2026-10-02 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-10-02 00:00:00 UTC to 2026-10-03 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-10-03 00:00:00 UTC to 2026-10-04 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-10-04 00:00:00 UTC to 2026-10-05 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-10-05 00:00:00 UTC to 2026-10-06 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-10-06 00:00:00 UTC to 2026-10-07 00:00:00 UTC (exclusive): 0 mentions; 0 submissions, 0 comments2026-10-07 00:00:00 UTC to 2026-10-08 00:00:00 UTC (exclusive): 2 mentions; 0 submissions, 2 comments2026-10-08 00:00:00 UTC to 2026-10-09 00:00:00 UTC (exclusive): 1 mentions; 0 submissions, 1 commentsOct 8

Counts come from the repository’s dated source evidence. Index cutoff: 2026-11-02 08:16:59 UTC.

View mention counts and date ranges
UTC ranges include their start and exclude their end. Select a period to filter the source evidence.
PeriodStart (UTC)End (exclusive, UTC)MentionsSubmissionsComments
Sep 82026-09-08 00:00:00 UTC2026-09-09 00:00:00 UTC404
Sep 92026-09-09 00:00:00 UTC2026-09-10 00:00:00 UTC716
Sep 102026-09-10 00:00:00 UTC2026-09-11 00:00:00 UTC101
Sep 112026-09-11 00:00:00 UTC2026-09-12 00:00:00 UTC312
Sep 122026-09-12 00:00:00 UTC2026-09-13 00:00:00 UTC101
Sep 132026-09-13 00:00:00 UTC2026-09-14 00:00:00 UTC101
Sep 142026-09-14 00:00:00 UTC2026-09-15 00:00:00 UTC000
Sep 152026-09-15 00:00:00 UTC2026-09-16 00:00:00 UTC000
Sep 162026-09-16 00:00:00 UTC2026-09-17 00:00:00 UTC000
Sep 172026-09-17 00:00:00 UTC2026-09-18 00:00:00 UTC000
Sep 182026-09-18 00:00:00 UTC2026-09-19 00:00:00 UTC000
Sep 192026-09-19 00:00:00 UTC2026-09-20 00:00:00 UTC000
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Sep 212026-09-21 00:00:00 UTC2026-09-22 00:00:00 UTC000
Sep 222026-09-22 00:00:00 UTC2026-09-23 00:00:00 UTC000
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Sep 242026-09-24 00:00:00 UTC2026-09-25 00:00:00 UTC000
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Sep 272026-09-27 00:00:00 UTC2026-09-28 00:00:00 UTC000
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Sep 292026-09-29 00:00:00 UTC2026-09-30 00:00:00 UTC000
Sep 302026-09-30 00:00:00 UTC2026-10-01 00:00:00 UTC000
Oct 12026-10-01 00:00:00 UTC2026-10-02 00:00:00 UTC000
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Oct 52026-10-05 00:00:00 UTC2026-10-06 00:00:00 UTC000
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Oct 72026-10-07 00:00:00 UTC2026-10-08 00:00:00 UTC202
Oct 82026-10-08 00:00:00 UTC2026-10-09 00:00:00 UTC101

What Hacker News says

20 sources
latent-person·Oct 8, 2026
In case you are not aware, the actual theorem statement of N-S was never translated by an LLM, but was written independently by formal conjectures, as they say in the README [1]. A Lean proof has a much higher probability of being correct (in my opinion) than any published (either preprint or peer-reviewed) paper, yet no one before LLMs were walking around claiming every result published can't be trusted yet (without an actual reason). We have seen one such instance of Lean bugs, which was found adversely against Lean (as in find bug then use this bug to prove Collatz, not just found when being asked to prove it). It's also worth to note that the way N-S (and all the other proofs by OpenAI etc) have been found is first prove it in NL then translate to Lean. I.e. it would have to first believe it found a correct proof in NL, and then after
Read the rest
wards either accidentally or on purpose use a Lean kernel bug. [1]: https://github.com/openai/NavierStokesAndEuler/blob/main/Com... edit: Probably also worth to mention that the proof have been checked both by the Lean kernel and the independent nanoda kernel, so it would need to exploit bug(s) from both.
In Navier–Stokes Lost in Translation
latent-person·Oct 7, 2026
> That's not a trivial if: stating the problem precisely is often as hard as the proof. Really? You think 300 lines of Lean code [1] is just as hard as the proof (or even remotely close)? Also note, as the README says [2], that the theorem was written independently by formal conjectures, not by the LLM. [1]:https://github.com/openai/NavierStokesAndEuler/blob/main/Com... [2]: https://github.com/openai/NavierStokesAndEuler/blob/main/Com...
In Navier–Stokes Lost in Translation
rawland·Sep 12, 2026
I ran the proof 3 days ago. They do a Comparator Challenge to validate that they actually solved the correct theorem from the result, which they copied from Google/DeepMind: https://github.com/openai/NavierStokesAndEuler/blob/f9e8bc5b... - this is valid for both Euler and NS. Also, they validated with an external kernel from the Lean Kernel Arena. That way bugs in the Lean kernels were found in the past already, iirc. Having said that, I strongly believe a positive result with the challenge above is the reason why they published it. I highly doubt anybody at OpenAI (or anywhere else) fully gets the proof after such a short time since publishing. This is also what Terry Tao criticized the most in my opinion. Independent of the remaining drama [0], from my point of view, the proof is correct and an achievement. [0]: https://news.ycombinator
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.com/item?id=49661928 - I am pretty much on the critical side, however, one can not ignore that it is an achievement. Esp. the unforced result.
In Navier-Stokes Announcement
1vuio0pswjnm7·Sep 10, 2026
09 Sep 2026 02:11:50 UTC | Statement from AMS Leadership on Navier-Stokes Problem | http://www.ams.org/news?news_id=7686 | https://news.ycombinator.com/item?id=49619946 | 1 comment 09 Sep 2026 03:02:22 UTC | Navier-Stokes Sebastien Bubeck | http://twitter.com/SebastienBubeck/status/209737941169151631... | https://news.ycombinator.com/item?id=49620327 | 3 comments 09 Sep 2026 07:04:58 UTC | Sam Altman's statement on the Navier-Stokes dispute | http://twitter.com/sama/status/2097385167002415140 | https://news.ycombinator.com/item?id=49622377 | 8 comments 09 Sep 2026 13:08:45 UTC | The Navier-Stokes solution for the legal profession | http://lexifina.com/blog/navier-stokes-solution-for-the-lega... | https://news.ycombinator.com/item?id=49625957 | 0 comments 09 Sep 2026 13:59:20 UTC | Navier stokes- Problem solution and the math for absolute
Read the rest
dumbfucks | http://x.com/kingofknowwhere/article/18 Jun 2036 22:40:17 UTC640886376 | https://news.ycombinator.com/item?id=49626706 | 0 comments 09 Sep 2026 14:39:38 UTC | OpenAI's 165-page Navier-Stokes proof failed a basic physics test | item?id=49627395 | https://news.ycombinator.com/item?id=49627395 | 0 comments 09 Sep 2026 16:28:57 UTC | To Serve Man: AI, Math, and NavierStokes | http://ml5885.github.io/writing/navier-stokes.html | https://news.ycombinator.com/item?id=49629132 | 2 comments 09 Sep 2026 17:33:47 UTC | Lean certificates accompanying Navier-Stokes and Euler results | http://github.com/openai/NavierStokesAndEuler/tree/main | https://news.ycombinator.com/item?id=49630159 | 0 comments 09 Sep 2026 18:54:55 UTC | NavierStokesAndEuler | http://github.com/openai/NavierStokesAndEuler | https://news.ycombinator.com/item?id=49632068 | 0 comments
In The Navier–Stokes Millennium Prize Problem
westurner·Sep 9, 2026
"Blowup for the Euler equations with smooth forcing" (2026) https://cims.nyu.edu/~tristanb/euler.pdf "Blowup for the Boussinesq equations with smooth forcing" (2026) https://cims.nyu.edu/~tristanb/boussinesq.pdf "Extending the Córdoba–Martínez-Zoroa IPM Blow-Up to Uniformly Spacetime Smooth Forcing" (2026) https://cims.nyu.edu/~tristanb/ipm.pdf "Finite Time Blowup for the Euler equation" (2026) https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194e... Lean proof: openai/NavierStokesAndEuler: https://github.com/openai/NavierStokesAndEuler
In Navier-Stokes – Tristan Buckmaster [pdf]
nayroclade·Sep 9, 2026
Prompting them yes, suggesting potentially fruitful research directions and so on, but the actual research was conducted by hundreds of agents swapping millions of messages and using billions of output tokens over 88 hours. The result being a huge Lean proof: https://github.com/openai/NavierStokesAndEuler. It's not just possible for humans to manually guide such a process in a meaningful way. They can set the direction and attempt to understand the result, but they solution itself must emerge (or not) from the agent swarm. So yes, the models do seem to be "solving" the problems themselves, but not necessarily in the way we think of mathematical discoveries happening. Academic mathematics has historically been resource constrained: There are a limited number of top-level mathematicians, and they only have so much time and brain power to sp
Read the rest
end. So when approaching a problem, they are essentially forced to be as efficient as possible, not just searching for a solution, but for one that can be achieved within their cognitive budget. This induces them to develop novel techniques and abstractions, and it is actually those techniques and abstractions that tend to be the valuable part for further research, not the proof itself. An agentic swarm is like getting a single skilled mathematician, cloning them a hundred times, then locking them in a room with the single objective of solving a problem. No longer constrained by time or brain power, they can approach it differently, using pre-existing techniques to gradually build their way to a solution. This process might not require a single intuitive leap or new discovery, and the solution will not be simple or elegant, but they will probably get there. It is more like a process of intelligently guided search than invention.
In How An AI math breakthrough ignited a controversy

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