AI Can Draft a Proof. It Can't Take Responsibility.

Key takeaways

• The claim that three OpenAI math papers were withdrawn remains unverified without the papers and their withdrawal notices.
• A single invalid step can undermine an otherwise convincing proof.
• Formal verification checks the encoded statement under its definitions and assumptions.
• Researchers and institutions remain responsible for checking results, explaining AI contributions, and correcting errors.

An AI-written proof can look impeccable right up to the line where it divides by zero. As AI takes a role in mathematical research, the central challenge is deciding what a result actually establishes—and who stands behind it.

Three withdrawals would still need an explanation

Consider the claim that three OpenAI mathematics papers were withdrawn. Before drawing conclusions, we need to identify the papers, read their withdrawal notices, and establish what “OpenAI papers” means.

A paper written by OpenAI researchers and a paper written by outside researchers using an OpenAI model involve different research teams. That distinction matters when assigning responsibility.

The reason for withdrawal matters, too. A fatal error in the central proof is different from a decision to revise or consolidate manuscripts. The word “withdrawn” alone doesn’t tell us which happened.

Then there is the model’s contribution. Did it suggest an approach, help with calculations, or draft the central argument? Even a confirmed withdrawal of an AI-assisted paper would not, on its own, establish that AI caused the problem.

Withdrawal status, withdrawal reason, and AI contribution are separate questions. Each needs its own answer before an individual case can tell us much about AI’s mathematical abilities.

One bad step is enough

A proof has to justify every step from its assumptions to its conclusion. Fluent explanations and impressive notation cannot repair a broken inference.

Take a simple example. Suppose a = b. Somewhere in the argument, we divide both sides of an equation by a - b.

Since a - b = 0, we have just divided by zero. Everything afterward might look tidy. The argument has still failed.

Research-level mistakes can be harder to spot. A proof might invoke a theorem without satisfying its conditions. Or it might take a pattern observed in several examples and quietly extend it to every possible case.

This is where a familiar software habit has limits. Testing a few inputs can catch errors and build confidence. It cannot establish a claim about infinitely many inputs by itself.

AI-written mathematics needs the same scrutiny as human-written mathematics. For every step, a reviewer should be able to identify the assumptions, the rule being applied, and why the conclusion follows. “Looks convincing” is a poor acceptance criterion.

A verified proof of which statement?

Formal verification offers a more rigorous way to check an argument. Researchers express a statement and its proof in a precise language, then use software to check the steps against specified logical rules.

That forces details into the open. A cancellation that requires a nonzero divisor needs a justification that the divisor is nonzero. Familiar-looking algebra gets no exemption.

But verification has a boundary: it checks the statement that was encoded, using the definitions and assumptions provided.

Suppose the original problem asks whether something holds for all integers. The encoded version asks only about positive integers. A valid proof of that narrower statement leaves zero and negative integers unresolved.

The proof checker can have done its job perfectly while the original problem remains unsolved.

Assessing a formally verified result therefore requires two checks: whether the proof passes, and whether the encoded statement faithfully represents the intended claim.

Responsibility stays with the people publishing

“We used AI” tells readers very little.

Researchers should explain whether the model supplied ideas, checked calculations, or drafted a proof. They should also describe how people reviewed the central argument. If formal verification was used, readers should be able to inspect the statement and assumptions that were checked.

When an error emerges, the explanation needs to be equally concrete. Which step failed? Which conclusions depend on it? Can the argument be repaired?

The researchers and institutions publishing the work are responsible for answering those questions.

Model developers have a related obligation when promoting mathematical results. They should explain the conditions under which a model succeeded and how much human intervention was involved. If people repaired and verified the argument, that contribution belongs in the account of the achievement.

A claim that AI solved a difficult problem should come with enough detail for others to check what was proved, under which assumptions, and who reviewed it. The lasting achievement is a proof that survives scrutiny. Responsibility for putting it into the world still has a human address.