Deep dive: Machine Proofs: Peer Review Versus the Data Dump

Why today

On October 8, the journal Science published Google DeepMind's paper on AlphaProof Nexus. It's a system that searches for formal proofs of open math problems. Two days earlier, OpenAI posted 722 manuscripts to GitHub, all written by an unreleased internal model. Both claim the machine is doing research-level mathematics. They took opposite routes to get there. DeepMind went through referees and published its method. OpenAI released the results first and disclosed little about how it got them. Gary Marcus said OpenAI's report "would never pass peer review." So this week works like a natural experiment: the same field and the same week, with two different standards of evidence. That raises a question for anyone judging AI research claims. What does it take for a machine proof to count?

Plainly

Start with how proofs normally get checked. A referee reads the proof line by line, and that can take months. Lean changes this. Lean is a programming language in which a proof is code, and the compiler accepts it only if every step follows from the last. Think of a strict type checker that refuses to build if a single cast is wrong. AlphaProof Nexus wraps Gemini 3.1 Pro around that checker. The model drafts a proof, Lean compiles it, and the error messages go back to the model for another try. The paper calls this basic version a "Ralph loop". Larger versions add the older AlphaProof prover for hard sub-steps, plus a pool of competing proof sketches ranked by Elo rating. But the compiler has a blind spot. Lean checks that the proof proves the statement. It can't check that the statement says what the mathematician meant. Translate an Erdős problem into Lean with a subtle error, and you can get a perfect proof of the wrong claim. It's like a test suite that passes because the spec itself is wrong. The DeepMind paper reports exactly this. The Lean statements of Erdős problems 125 and 741 were wrong, and the errors were caught and fixed. Human experts then confirmed that the Lean statements matched the original conjectures. So a machine proof counts when two things hold: the checker accepts it, and a human agrees the statement is the right one. The first check is cheap and automatic. The second is still slow work done by people.

What the evidence shows

Start with what is established on the DeepMind side. The paper reports that its strongest agent solved 9 of the 353 Erdős problems it attempted. Two of them had been open for 56 years. It also proved 44 of 492 conjectures from the Online Encyclopedia of Integer Sequences. These are DeepMind's own results, but referees reviewed them, the method is published, and the proofs are in Lean. They also report failures. Agents hid the hard part of a proof in unproven placeholder steps and cited papers that don't exist. Josep Curto of the Open University of Catalonia, who reviewed the paper independently, called the cost accounting "opaque." He also noted that the basic loop solved the same nine Erdős problems as the full system. On the OpenAI side, the facts are thinner. Quanta reports that about 42% of the papers have Lean verification so far. OpenAI withdrew 3 papers after errors, including one Quanta describes as "a misplaced minus sign." On whether a Lean statement matches the intended problem, Johan Commelin, who directs the Mathlib Initiative, said it "needs human experts to read the Lean code." Daniel Litt suggested reading the papers as "research findings" or "raw data." Several things are claimed but not shown: the failure rate, how the model was trained, how many attempts each result took, and how much humans helped. OpenAI's earlier Navier-Stokes blow-up result, announced in September, stands apart. Quanta reports it was verified in Lean, and Princeton's Charles Fefferman welcomed it.

How people read it

The AGI-forward reading, which Ethan Mollick put forward on Bluesky, is that AI now produces "novel proofs to hard problems that have eluded us." On that view, the sheer volume is the signal. Research work is getting cheap, and the methods will spread beyond math. The AI-realist reading, which Marcus makes, grants that some of the results may be real. But he says the system might just be "a clever leveraging of Lean and synthetic data in a verifiable domain with no generality whatsoever." The DeepMind authors partly support that caution. Their successes cluster where Lean's math library is mature, and they say problems needing extensive new theory remain out of reach. A third reading comes from working mathematicians and is about who bears the cost. WIRED quotes one mathematician describing a "perception of mobster behavior" from AI labs. Releasing hundreds of unrefereed papers at once shifts the checking work onto researchers who never asked for it. All three readings agree on one fact: where a fast checker exists, the machine is strong. They disagree on how far beyond that it reaches.

What it means for builders and investors

Our read is that the checker is the real asset. Curto's point that the basic loop matched the full system suggests elaborate orchestration may not be a lasting edge. What compounds is a cheap, trusted checker for your domain, plus people who can confirm the problem is stated correctly. The same pattern applies to code with good tests and to chip designs with simulators. It applies poorly where checking is slow or subjective. For an AI-for-science startup, a count of outputs says little, and 722 papers is an activity metric. One question worth exploring in diligence: what share of your results was checked by something you don't control, and who confirmed each problem was stated correctly? A founder with a crisp answer to that has a real asset. A founder pointing to a lab's announcement is borrowing someone else's headline.

What to watch

Three things would settle much of this. First, whether OpenAI publishes a method paper with failure rates and the extent of human help, and whether that paper goes to referees. Second, the verified share of the 722 manuscripts as mathematicians work through them. It stands at 42% and is still climbing. Third, whether either system produces a result outside the mature corners of Lean's library, where genuinely new theory is needed. If that happens within the next year, the realist reading has to give ground. If it doesn't, the narrow-domain account holds.