Adib Rahman

Assistant Professor of Practice (Economics) at Arkansas State University

[Valerio Capraro @ValerioCapraro]

BREAKING: OpenAI’s solution to Navier–Stokes does not match its Lean verification.

The most important article to read today is not one of OpenAI’s 700 AI-generated math papers.

It is this other paper, making a deep and worrying point:

A Lean-verified proof does not automatically validate the proof written in natural language, nor does it mean that the formal statement captures the intended theorem.

During translation, an AI can change an assumption, weaken a statement, or replace the argument entirely.

It can hallucinate another theorem.

Lean correctly verifies the result.
But the proved result may no longer be what the paper claims.

This is a general problem. Things get spicy when the authors examine OpenAI’s proposed Navier–Stokes solution.

They identify at least two mismatches between the written intermediate results and their Lean counterparts:

One estimate claims that four additional input derivatives suffice. The Lean version requires five: a weaker result.

A pressure-flux estimate is obtained through a different bound, and proved through a different argument.

It is not clear whether these mismatches invalidate the entire proof.

But they raise an important issue.

OpenAI is flooding us with claimed revolutionary breakthroughs. Yet nobody knows whether the proofs are correct or whether they prove what they claim to be proving.

Epistemia at scale.

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Paper in the first reply

[Adib Rahman @rah90994524]

@_AlvinChristian I am teaching this next week haha. I really like this firm side of micro

[Adib Rahman @rah90994524]

@auyonymous @MahdiKahou Ben Affleck is after your job now 😉

[Adib Rahman @rah90994524]

@MahdiKahou Gotta keep our jobs!

[Adib Rahman @rah90994524]

@MahdiKahou Very well said. And also this would be hard to do so in macro with so many disagreements on the modeling choice. AI is useful for calibration in macro but it is not good at coming up with its own theoretical model. There are many subtleties in a macro model.

[Adib Rahman @rah90994524]

@alz_zyd_ AI will save the pure math market! More mathematicians will be hired to verify their proofs

[Adib Rahman @rah90994524]

@RenaudFoucart @40yoap @raincoin_ Call me when the economy is failing! But can't guarantee if my models will help 😕

[Adib Rahman @rah90994524]

@scottgrvs @PI010101 Open AI will hire more mathematicians to verify their AI proofs.

[Henry Shevlin @dioscuri]

holy shit ChatGPT is actually developing humanlike academic skills

[Adib Rahman @rah90994524]

@auyonymous @_cingraham It’s a bit offensive, IMO, but I’m glad you’re seeing the funny side of it. He was probably just making a poor attempt at trolling you

[Adib Rahman @rah90994524]

@40yoap @RBCtabris Too bad that people are cutting down on their discretionary spending as a result of rising rates

[Adib Rahman @rah90994524]

@AlexZevelev Okay that's Newton, but what about Leibniz though??

[Adib Rahman @rah90994524]

@40yoap @wwwojtekk Btw there are many typos and mistakes in the MWG solutions manual.

[Adib Rahman @rah90994524]

@40yoap @wwwojtekk Someone should use AI to work out all the solutions to Rudin's textbook, and publish a solutions manual. Same goes for the MWG textbook in Micro.

[Adib Rahman @rah90994524]

@aledinola @40yoap @wwwojtekk Oh nvm the Jehle and Reny solutions were handwritten by someone.

The MWG solutions were prepared by Hara, Segal, and Tadelis. But yes, they are not in a nice PDF format with Latex typesetting.

[Adib Rahman @rah90994524]

@aledinola @40yoap @wwwojtekk There used to be an MWG solution online, and it may still exist. However, it was handwritten and scanned by someone (or a group of people). I would prefer it if it were available as a proper PDF with Latex typesetting.

[Adib Rahman @rah90994524]

@40yoap @aledinola @wwwojtekk Yes, you are correct!

[Adib Rahman @rah90994524]

@40yoap Meh I would rather neetmaxx

[Adib Rahman @rah90994524]

@gguillaumeblanc Btw I would be wary of uploading a submitted manuscript to Pangram, as this may also go against a journal's LLM policies given that one has accepted to review the paper. Uploading a working paper may be fine, but I'm not 100% certain.

[Adib Rahman @rah90994524]

@gguillaumeblanc Meh at least it's not 100% AI