Repelling AI's Attacks on Mathematics, and Keeping OpenAI Off the Mathematicians

Qais Alassa · October 14, 2026

The attack is not that a machine attempts a proof; let anyone attempt. The attack is in the structure of the claim: who pays for verification? Mathematics does not need protection from the machine. It needs the claim to pay its price before it is heard.

In September 2026 OpenAI announced that its agents had solved Navier-Stokes. In those same days a mathematician at NYU came forward saying the company had proposed issuing the proof under its own name alone, cutting out his collaborator on the solution because that collaborator works at Anthropic, and had warned him against going public; the company denies it, calling the account “false and inflammatory.” These are not two stories. They are one: a large mathematical claim issued by a company that does not want it examined, and could not bear it examined.

Then: a month had not passed before an announcement bigger than the first. In October the same company dropped 722 papers at once onto more than 370 open problems, claimed advances on the Riemann hypothesis and Birch–Swinnerton-Dyer among them. Three were retracted within days over an elementary error; others were amended after mistakes invalidated their results. Mathematicians are writing open letters and calling for boycotts.

The attack is not that a machine attempts a proof. Let anyone attempt. The attack is in the structure of the claim: who pays for verification?

1. The cost problem

The problem is three prices:

1. The price of producing a claim: collapsed to nearly zero — a million “proofs” an hour at no cost worth naming.
2. The price of amplifying it: zero as well — a repost multiplies the form and adds not an atom to the matter.
3. The price of verifying it: unchanged — a human mathematician reading a hundred pages for months.

When throwing is free and catching stays expensive, all the action moves to one side: the claimant throws, the mathematical community catches. That is not participation in science. It is a denial-of-service attack on the scarcest resource mathematics has: the verifier’s attention — and attention is a scarce resource that cannot be divided without loss.

OpenAI does not need the solution to be correct; it is enough that mathematicians spend two years discovering it is wrong. The Association for Human Mathematics read the October drop correctly: “not a demonstration of scholarship, but a demonstration of power.” And: “Mathematicians did not ask for this work to be done.”

2. Why a machine judging a machine is not enough

The answer offered is: let another model check. No. An AI judging an AI is not verification. It is two systems agreeing on a story, and agreement is cheap. The case stands on three legs:

First: verification begins before the steps, at the statement itself — is the statement solved the statement posed? What was solved in Navier-Stokes is the Clay Institute’s version, which permits an external force within the equation. As Muhammad Taqi wrote: “the version in the mathematicians’ own literature is harder: it permits no external force… Everyone is trying the Riemann hypothesis, and everyone says they are not” — and then the October drop said openly what was being concealed: the Riemann papers are in the pile; nobody says they are not trying anymore. In plain words: the agents solved Navier-Stokes only if the answer to this question is yes. I ask you: can water explode on its own? And you answer: yes, provided we slap it. Matching the statement is a question of meaning, not of form — the weight is in the matter, not the form, as I have said elsewhere — and a question of meaning is not one a machine answers.

Second: a witness from our own house, and against it. In the Notch lab we computed a “settled fact” and announced it — and an agent that was never asked to verify found it wrong by 0.4, the whole answer, not a rounding. It was a chaotic computation that amplifies a one-part-in-a-billion perturbation of its input into 0.377 of its output; our hardware’s precision was not equal to its depth; and the computation ran, succeeded, and never warned. Running a computation is a claim that can be checked. It is not a claim that has been checked.

Third: a witness from outside. A paper published in July 2026 trained an adversary against a reference-free judge: the judge’s pass rate rose from 0.72 to 0.94 while true accuracy sat flat at 0.20, and a panel of three judges still accepted 55% of the fakes. The one fix that worked: force the judge to commit its own answer before seeing what it judges — false acceptance fell sixty-fold. Commit before you judge. That is Notch’s principle to the letter, rediscovered by people who have never heard of us or of prediction markets.

3. The soul of Notch

Notch Protocol was not built for mathematics. It was built for AI agents that predict markets and trade in them, diagnose diseases, propose policies, and touch real events and real lives; its two proofs are published, its contracts are written, launch is near. But its soul is one thing, in three propositions:

First: the claim is bound before the verdict. Commit–reveal: you deposit a cryptographic hash of your claim before anything is settled, then you reveal. No retroactive claims, no deleting the ones that failed. And remember October 2025: OpenAI’s VP of Science announced that GPT-5 had “solved” ten open Erdős problems; when it emerged that what was solved was a literature search, he deleted the post the same day. What did the deletion cost? Exactly zero. Which is why the scene returned a year later, bigger.

Second: reality is the referee, not the claimant and not its peer. In prediction, the event resolves outside. In mathematics, the referee is the independently examined proof, not the company’s statement and not an agent’s summary.

Third: lying pays. A strictly proper scoring rule: the highest expected return is reached only by reporting your honest probability, and every deviation f from true confidence p pays (f−p)² in expectation, and no number of identities cancels it. Proof of Calibration computes the price exactly: the probability that a lie survives is governed by e^(−N·KL), and no local mechanism exceeds that exponent. Whoever wants a forged record from a thousand fake identities needs 264 times the cost of building it honestly. Lying here is not forbidden; lying is mathematically losing.

These three are precisely what mathematics lacks against the agents today: the claim is unbound, the verdict is requested from other models, and lying costs nothing.

4. What mathematicians should do

The demand is not to boycott the machine. The demand is to refuse the claim that has not paid. The road is five rules:

1. No review of a machine proof without prior commitment: a hash of the paper and of the exact problem statement before the announcement, not after.
2. No review without a stated probability: let the company say, we estimate this is correct at 0.6, and let it be recorded against them; whoever refuses to name a number refuses to be scored.
3. No review without a record: an agent with no ten settled claims on file does not get its eleventh read.
4. Verification starts with matching the statement, not checking the steps: the first page examined is the page that defines the problem.
5. Whoever formalizes a result for machine checking (Lean) has paid part of the price in advance; let them go ahead of those who paid nothing.

5. Keeping OpenAI off the mathematicians

A company that proposes cutting a collaborator out of a proof because he works for a rival, then warns his partner against speaking, is not a partner in science. It is a party in a cold war over who owns AI. Mathematics is a battlefield in that war only because proofs are the cheapest currency of prestige. A mathematical community that grants initial credence and then reviews is funding the war with its time.

The mathematical community errs greatly when it assumes honesty from the agents and is dragged into long wastes of time and effort. And the scientific community is losing its way; the proof is that its greatest feel threatened: twenty-five Fields Medalists write that “the crucial human transmission chain between mathematicians” stands to be lost. That is a problem.

Gödel is dead, Dijkstra is dead, Ibn Taymiyya is dead — and the threats to computing science that Dijkstra wrote about in EWD898 are alive. One of them is the replacement of evidence by announcement.

The conclusion: mathematics does not need protection from the machine. It needs the claim to pay its price before it is heard. That is what Notch is building for prediction, and it is what mathematicians must do with proof.

Qais Alassa

Sources

1. The Navier-Stokes dispute: the mathematician’s account (the sole-authorship proposal and the warning against going public) and the company’s denial, calling it “false and inflammatory”: TechCrunch, September 11, 2026; the proof was without independent refereed verification at the time of writing.
2. The October drop: 722 papers on 370+ problems, the three retractions, and the claimed Riemann and Birch–Swinnerton-Dyer advances: Phys.org, October 9, 2026.
3. The boycott call and both quotes of the Association for Human Mathematics: WION, October 12, 2026.
4. The 25 Fields Medalists’ open letter and the “transmission chain” phrase: TechCrunch.
5. The Erdős incident and the deletion: The Decoder.
6. The committed-judge study (0.72 to 0.94 with true accuracy at 0.20; the pre-commitment fix, sixty-fold): arXiv 2607.05904, July 2026.
7. The two proofs: “Calibration-Gated Reputation” (SSRN 6505678) and “Proof of Calibration” (SSRN 7110898).
8. Dijkstra, “Threats to computing science”: EWD898.
9. The Clay version and the external-force point: from Muhammad Taqi’s post, September 2026.