AI Cracks 87-Year Math Problem With Formula Fit for a Tweet

Sometimes the biggest breakthroughs come in the smallest packages.

Levent Alpöge, a mathematician at AI company Anthropic, just cracked a math problem that's been puzzling experts since 1939. He did it with help from Claude Fable 5, an AI that only launched a few weeks ago, and the answer was shockingly simple.

The Jacobian conjecture has been math's version of a locked door for 87 years. It deals with functions, which are like machines that move points around in space using equations. The conjecture said that if a function moves space around "nicely" without crushing points together, you should always be able to reverse it and put everything back where it started.

Mathematicians have been trying to prove or disprove this idea across different dimensions since German mathematician Ott-Heinrich Keller proposed the general version in 1939. Two famous 20th-century mathematicians thought they'd solved it, but subtle errors invalidated both attempts. The problem even made a prestigious list of Mathematical Problems for the Next Century in 1998.

Here's what made this discovery so remarkable. Alpöge found a counterexample in three dimensions that proved the conjecture wrong. His function has all the "nice" properties but still can't be reversed because it merges some points together. And the entire formula was short enough to post on social media.

Other mathematicians quickly verified the answer because of its simplicity. A 2017 online comment predicted exactly this scenario, joking that "some smart undergraduate can simply write a formula" to crack the case. That's essentially what happened.

Why This Inspires

This breakthrough shows AI isn't just about replacing human creativity. It's about amplifying it. Alpöge combined his mathematical expertise with AI's ability to spot patterns humans might miss, creating a powerful partnership.

The discovery joins other recent AI-assisted math wins, including solutions to the unit distance conjecture and a problem posed by legendary mathematician Paul Erdős. These tools can pull ideas from different areas of math and combine them in novel ways, opening doors that seemed permanently locked.

The original two-dimensional version of the conjecture remains unsolved, giving mathematicians a new puzzle to tackle with their AI partners.

Progress sometimes arrives in unexpected packages, proving that the next big answer might be simpler than anyone imagined.