Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs · HackerPapers discussions

Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by tarsierscripter

Tue, 03 Nov 2026 18:58:55 GMT

Many of the proofs released by Open AI don’t have Lean proofs. Their system doesn’t work in Lean directly, it writes proofs in natural language first. Later, some of the proofs were passed through an auto-formalization model to generate Lean code which then passed Lean’s checks. The issue is that the auto-formalization step itself is not trivial. There is no formal verification which proves the translation correct, so it is up to mathematicians to hand-check the formalization to make sure it’s saying the same thing. Unfortunately, this problem is undecidable in general. We’ve already had a…

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by paulceton

Sat, 17 Oct 2026 06:08:48 GMT

I’ve been a math professor for about ten years, and I think people outside the field misread what makes mathematicians angry, sad, and worried. Interviews that make it into the media tend to go with “AI is killing mathematics,” maybe because that gets clicks. The reality is more complicated. Some mathematicians work on well-posed, famous problems, but most mathematical research is about questions that aren't well-posed yet. A typical example is finding where the boundary of existence lies for some equation: which meaningful conditions guarantee a solution, and how far can you weaken them? You…

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by tomkeen

Sat, 10 Oct 2026 12:02:28 GMT

The paper is "Navier–Stokes lost in translation" by Bastounis, Circelli, and Hansen (Cambridge/DAMTP): https://arxiv.org/abs/2610.08144

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by jey

Sat, 10 Oct 2026 00:24:35 GMT

This headline is completely wrong. The proper coding analogy is more like, the natural-language paper was the "design document" before coding it up, then when coding it up as Lean4 proofs, specific details were realized to be slightly off[1] and corrected while writing the implementation in code as machine-checkable proofs. Which I'm sure is an extremely relatable situation for most of us here. But the paper or "design document" wasn't corrected afterwards. I also think this "paper then code" approach is now obsolete. The modern way, in AI-assisted workflows, is to first iterate on…

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by gregw2

Fri, 09 Oct 2026 20:23:08 GMT

I read somewhere that 56% of the problems had some Lean Proof, but upon inspection, there are gaps between what Lean proves and what English says about the proof. Making an English language description of a problem and proof steps match the Lean proof is apparently harder than the halting problem and is not something that a Lean proof alone or the current dump or even the Navier-Stokes dump solves. A good breakdown of the problem is here: https://arxiv.org/html/2610.08144v1 or also see here: https://terrytao.wordpress.com/2026/10/09/what-mathematician...

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by pierreb-aiva

Fri, 09 Oct 2026 15:05:25 GMT

Until models have taste, we still need Software Engineers to judge their output in the context of a broader goal. Not saying this will never happen, but we have yet to see evidence of models getting good at this. If anything, the lack of improvement on that axis has been quite underwhelming; the latest example of that being OpenAI offering a Lean proof of the solutions to the Navier-Stokes equations, but that proof not matching the natural language of that proof [1]. [1] https://arxiv.org/html/2610.08144v1

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by persedes

Thu, 08 Oct 2026 16:05:18 GMT

> All the human needs to verify is that the statement of the theorem is translated correctly from natural language to Lean. That usually covers a very small surface of the Lean code. That's exactly what the navier stokes paper posted yesterday pointed out where the LLM bends the Lean code to make it "compile", because the NL might be wrong to begin with or because it missed a detail: https://arxiv.org/html/2610.08144v1#S2 For complex / tedious proofs I can easily see how small details like this can lead to a valid lean proof (or valid "code"), but missing the important details that got lost.

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by ijustlovemath

Thu, 08 Oct 2026 16:03:31 GMT

Oh I fully understand how Lean works, how minimal the kernel is etc. I just think that just because "it compiled", we don't actually know that the autoformalization proved all the right stuff along the way. After all, LLMs can produce correct proofs for statements that don't align with the original intended theorem [1]. I just think we should be a bit more skeptical in general before saying these seminal results are fully true. What's the rush? [1] - https://arxiv.org/abs/2610.08144

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by cmceanga

Thu, 08 Oct 2026 10:45:10 GMT

There is no guarantee that the lean proof is 1:1 with the natural language equivalent. The lean proof can be lesser. This happened in the Navier-Stokes proof, e.g. see [1] in example 3.1. Having the certificate doesn't necessarily imply correctness. [1] https://arxiv.org/abs/2610.08144

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by dualvariable

Wed, 07 Oct 2026 21:36:54 GMT

In addition to those issues that the wife in the story raised, here's some meta-analysis of the Navier-Stokes result that puts all of these solutions into question: https://arxiv.org/abs/2610.08144 > Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this process, an AI system translates the text from a natural language (NL) into a formal language such as Lean. Once this translation is done, the argument expressed in the formal language can easily be…

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — mentioned by nperez19

Wed, 07 Oct 2026 20:28:42 GMT

There's an entire paper claiming that many of these AI-generated Lean proofs are formulated incorrectly / mistranslated: https://arxiv.org/abs/2610.08144

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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs — HN submission

Wed, 07 Oct 2026 15:24:38 GMT

Navier–Stokes Lost in Translation

361 points; 240 discussion replies on HN. Paper and source history. A submission is not an endorsement.