Claude Fable 5 breaks an 87-year-old math conjecture

Mathematicians have been scratching their heads over a notorious algebra riddle since 1939. Some thought humans wouldn't crack it for another century. Then, over the weekend, an AI basically solved it as a side quest while everyone was watching the World Cup.

Anthropic researcher Levent Alpöge took to X with a hilariously casual post, revealing that Claude Fable 5 produced a one-line formula that breaks the famous Jacobian conjecture.

Alpöge thanked his close friend Fable for putting in the work during the World Cup final, treating a monumental breakthrough like a light weekend project.

The one-line counterexample

The Jacobian conjecture has puzzled the mathematics world for decades, with many ambitious attempts crumbling under peer review.

Back in 2008, famed mathematician T.T. Moh predicted that finding an answer could easily take humans another 100 years.

While previous claims eventually unraveled due to hidden flaws in massive, multi-page arguments, this one is different. Experts say Fable's output is so remarkably short that it can be confirmed directly on the spot.

This adds to an unprecedented streak of frontier-model wins in mathematics this year, following the resolution of several open Erdős problems and OpenAI tackling the 80-year-old unit distance puzzle.

Why it matters

What makes this development wild is not just that a decades-old math problem fell, but the effortless way it happened.

For researchers and developers, this changes the playbook. AI is moving past being a glorified research assistant that summarizes papers or writes boilerplate code. It is now actively probing extreme edge cases in pure logic and handing humans verified counterexamples that fit on a single line. You might not have direct access to Fable 5 today, but the fact that models can bypass a century of human dead ends with pure computation is a massive signal.

Across the industry, this reignites the debate on machine reasoning. Critics have long argued that LLMs merely parrot statistical correlations, but constructing a valid counterexample in advanced algebra requires deep structural accuracy. When verification is this trivial, the speed of scientific discovery changes completely.

In our view, Fable's approach is brilliant because it avoids the traps of bloated, hundreds-of-pages-long mathematical proofs. The catch, however, is that while an AI can pinpoint a rogue formula that breaks a conjecture, it does not necessarily provide the grand unifying intuition behind why it exists. Humans now have to reverse-engineer the insight.

Still, when an AI casually knocks down a historic 1939 problem during a soccer match, picturing where frontier models will be in another year or two feels genuinely mind-bending.