AI repaired the proof. Was the original right?

Researchers deliberately gave an AI a faulty argument. They report receiving a corrected Lean proof that passed. [1]

Try zero in both expressions

The researchers deliberately miswrote p(x)=x³−x²−x+1 as (x−1)(x+1)². The goal was to show that p(x) is nonnegative whenever x is at least −1. [1]

Replace every x with zero. In the original expression, 0³−0²−0+1=1. The product gives (0−1)(0+1)²=−1. Equivalent expressions must give the same value. Since 1 and −1 differ, that step is wrong. Zero is at least −1, so the check stays within the stated conditions.

Squaring means multiplying a number by itself. The square belongs on x−1. Substituting zero into the corrected expression, (x−1)²(x+1), gives (−1)×(−1)×1=1. This exposes the faulty step of rewriting the expression as a product. It does not refute the target statement p(x)≥0 or the final Lean proof reported by the researchers.

Which sheet gets the stamp?

Lean is a language for writing statements and proofs that a computer can check. Its official guidance distinguishes establishing a proof from understanding what its statement means. The definitions and axioms used also need attention. [2]

Place the original sheet and the revised sheet side by side on a desk. After a faulty line is repaired, the approval stamp lands on the revised sheet. Reading that stamp as approval of everything on the first sheet overlooks the change between them.

What the two sources address

On 8 September 2026, OpenAI announced its Navier–Stokes result, releasing a written proof and Lean formalization. It reported an additional 17 hours for formalization and verification. That is the announcing party’s account. [3]

In their 6 October preprint (v1), Alexander Bastounis, Fabian Circelli and Anders C. Hansen question fidelity between original arguments and formalizations. They explicitly leave the correctness of OpenAI’s original Navier–Stokes proof undecided. [1]

V’s view

If AI is a partner for repairing an argument, a correction can be a welcome achievement. If its job is to review the original, both versions should be retained. I would find the technology more useful with a change record beside the approval mark. Readers could then assess the repaired solution and the starting idea on their own merits.

A short limitation

This article checks a simple substitution alongside the public preprint and official explanations. It does not run Lean or reverify the complete Navier–Stokes proof. Completion of peer review for the preprint was not established here.