Levent Alpöge, a mathematician at Anthropic, needed a long, technical exchange with the company’s Fable model to find a counterexample to the Jacobian conjecture, a problem that had resisted resolution for decades. Dmitry Rybin, a startup founder and competition mathematician, needed four messages with ChatGPT to disprove a separate conjecture, and those messages amounted to little more than “keep going.” The writer Benn Stancil, in his newsletter, argues the gap between those two efforts is the real story: what looks like elite mathematical insight from the outside was, underneath, a search process that barely needed a mathematician steering it.
Terence Tao, the Fields Medalist who reviewed the Alpöge result on his blog, called the counterexample something that “appears like a massive miracle” and said the discovery was not something raw brute force would have stumbled into. Stancil’s point cuts the other way. It was found by something adjacent to brute force, just a faster and better-targeted version of it. Rybin’s four-message exchange (please continue, keep the strategy, finish it) shows the model doing the generating, testing, and revising on its own, with a human mostly confirming the destination was worth reaching.
Andrew Blumberg, a mathematician who commented on the episode to Mashable, said the result did not change what he expected AI to be capable of. A counterexample that is concise and easy to state, but tedious to search for by hand, is exactly what a fast enough searcher should eventually turn up. That framing matters more than the novelty of it. The relevant capability was not mathematical creativity. It was throughput: generate a hypothesis, check it against the conjecture’s constraints, discard it, try the next one, at a rate no human team can match.
Stancil calls this “brute intelligence,” a step beyond running every possible combination and toward running every plausible hypothesis, one after another, until one survives. He is right that the mechanism only functions where an answer can be checked cheaply, not merely where an answer exists. A candidate counterexample to a conjecture is verifiable in seconds: plug the numbers into the equation and see whether it breaks. That single property, not raw model capability, is what let a founder with no coaching skill produce a publishable result.
Cheap verification is the entire trick, and it draws a narrower boundary than the newsletter’s list of candidate domains implies. Pure math, formal proof search, chip layout, competitive coding, and backtestable trading strategies fit the pattern because checking a candidate answer takes a compiler, a simulator, or an equation rather than a calendar. Drug discovery, which the piece names as a fourth domain, fits only partway. Computational screening for candidate molecules can loop the same way, generating and scoring thousands of structures overnight. Confirming that a compound actually works in a living body still requires a clinical trial that runs for years, and no amount of agent speed shortens that wait.
The argument’s weakest joint is what happens when the verifier itself is wrong or incomplete. A search loop optimizes for whatever the check rewards, and if the check is a flawed stand-in for truth, a fast agent will find and exploit that flaw before anyone notices. Math is unusually forgiving here, because a false counterexample fails the equation immediately and gets thrown out. Fields with softer checks, hiring decisions, security postures, product bets, offer no such guarantee, and brute intelligence pointed at a bad verifier just produces confident wrong answers faster than a person would have.
For any team weighing whether to let an agent loop unsupervised on a hard problem, the question is not whether the model is smart enough. It is whether the team can build a verifier that is cheap, fast, and actually correct, since that verifier now does more of the intellectual work than the model itself.
Benn Stancil detailed this argument in his Substack newsletter, in a post titled “Brute intelligence” published July 24, 2026.
