John Loeber built his own automated theorem prover this year, and in an essay on his Substack, “John Loeber,” he describes how successive OpenAI models made nearly all of that engineering beside the point. It is a first-person case study in the bitter lesson, the old argument that general methods riding on more compute beat hand-built cleverness, landing on one builder’s weekends.
Loeber has followed machine learning and mathematics since 2013. His bet was that proofs had to be written in Lean, the formal verification language, from the start, because he doubted a model could hold a correct argument together over dozens of pages of plain text. So he forked Lean4 for faster proof search and wrote a harness that split strategies across many subagents. He says the stock Claude Code and Codex harnesses lost track of long context and cost too much. He added C++ programs to hunt for counterexamples, plus tooling for distributed compute, rate limits, and a searchable cache of lemmas.
The system worked, slowly. With GPT-5.5 it produced some novel lemmas, along with plenty of incoherent statements. GPT-5.6 Sol proposed better strategies, and Loeber wrote several hundred thousand lines of Lean in pursuit of two targets: the Moore graph question for degree 57, and the Hadwiger Conjecture. Every promising reduction stalled just short of closing. He notes that he ran no private evals, so the improvement he describes is his impression, nothing measured.
Then came GPT-6 Astra, and a few days later, by his account, the Navier-Stokes smoothness question fell. He stopped working. Four weeks after that, OpenAI pointed an unreleased model at 4,000 major problems, giving each about 3.5 hours of Pro-tier ChatGPT thinking time on average. Loeber puts that at maybe $100 each, at most, which is his own estimate. The published math repo claims hundreds of major results, including a disproof of Hadwiger. He had spent his effort trying to prove it.
That disproof, he points out, offers no explicit counterexample. It argues probabilistically that a counterexample graph exists.
The detail that unsettled him most concerns method. Loeber reads the release pattern as showing that the models wrote their proofs as plain text and that only about half were formalized in Lean afterward, which means about half of the claimed results have no accompanying Lean proof. He labels this unconfirmed, since he has not asked anyone at OpenAI or Anthropic. If it holds, the strategy he built around, formalizing as you go to keep the model from drifting, was a crutch the models no longer needed.
Everything in the essay rests on one participant’s memory and OpenAI’s own repository. No independent group is cited as having checked the claimed results, and the model names and timeline are Loeber’s telling. What carries weight is the vantage point: a capable engineer who spent real effort on the problem, with no incentive to flatter the labs, reports that his tooling was overtaken by base-model gains. He has not even open-sourced it, calling the cleanup pointless.
His conclusion is more upbeat than the story suggests. Loeber says a working mathematician’s chance of a major result has gone from slim to zero, so the field now resembles the humanities, valued for the pleasure of understanding. He counts the window of human and AI collaboration as a single summer. He calls the trade good and expects the same pattern in other disciplines.
For anyone selling a specialized wrapper around a frontier model, the number to hold is the one Loeber guesses: about $100 of compute per hard problem. That is the price his months of engineering, and any similar scaffolding, now has to beat.
Reported by John Loeber on his Substack, essays.johnloeber.com, in the essay “Bitter Lessoned in Automated Theorem Proving” (no publication date given in the source).
