An AI Helped Disprove an 87-Year-Old Math Problem Over the Weekend
Over the weekend, mathematicians used Anthropic's Fable 5 model to find a counterexample to the Jacobian conjecture, a famous question open since 1939. What actually happened, and why 'an AI did maths' does not mean what the headlines suggest.
Over the weekend, a famous maths problem that had stood since 1939 fell, and an AI model was in the room when it happened. Mathematician Levent Alpoge announced that the Jacobian conjecture is false, and credited Anthropic’s Fable 5 model with doing the heavy lifting while he watched the World Cup final. Terence Tao, widely seen as one of the greatest living mathematicians, has since published a write-up walking through the result. Interestingly, an OpenAI researcher said an internal version of the company’s Codex model found essentially the same counterexample on its own.
A quick translation, because the jargon hides a simple idea. A “conjecture” is a statement mathematicians believe is true but have not proven. To “disprove” one, you do not need a grand theory; you need a single “counterexample,” one concrete case where the statement fails. That is what the model produced: a specific example that breaks the conjecture. And crucially, once it existed, human mathematicians could check it by hand within a day. The AI did not ask anyone to trust it. It handed over an answer that stands or falls on its own.
This is now the second such story in a week. In mid-July, another model was reported to have knocked over a decades-old statistics puzzle. A pattern is forming, and it is worth understanding rather than hyping. These models are getting genuinely good at a particular kind of task: searching a vast space of possibilities for a clever construction that a human might take years to stumble on. That is not the same as “understanding” mathematics, and it is not general intelligence. It is a powerful search tool pointed at problems where any proposed answer is cheap to verify.
What this means for you: If you are not a mathematician, the practical impact today is roughly zero, and that is honest rather than dismissive. But the shape of it matters. The most trustworthy way to use AI on hard problems is exactly this: let the model propose, let humans (or a computer) verify. When the answer can be checked, it does not matter that the model occasionally makes things up, because a wrong counterexample simply fails the check. That principle, use AI to generate, keep a cheap way to verify, is one you can borrow in far more ordinary settings, from code that has tests to a claim you can look up. A fair caveat: “AI cracked a maths problem” makes a better headline than “AI proposed a candidate that a human expert then verified,” but the second version is the accurate one.
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Source: https://thenextweb.com/news/jacobian-conjecture-disproved-ai-fable-5
Anthropic Says It Rewrote a Million Lines of Code in Two Weeks Using Its Own AI
Anthropic published how its engineers used Claude Code to port huge codebases between programming languages in weeks instead of years. Impressive, genuinely useful, and a good window into what AI coding is actually good at.
