Fable disproved an 87-year-old conjecture
Fable disproved an 87-year-old conjecture
Mathematicians Levent Alpöge and Akhil Mathew asked the model to find a counterexample to the Jacobian Conjecture from 1939. Claude Fable 5 came back with a short formula. And it actually works.
In plain English, the conjecture said that if a complicated mathematical transformation never breaks, you should always be able to reverse it. Fable’s formula pulls a trick: three different points collapse into one. You can’t reverse that, because there’s no way to tell which point you started from. So the conjecture is false, at least in three dimensions.
Instead of pages of AI slop, this is a concrete formula anyone can check. Drop it into another model with Python, SymPy, or Wolfram and ask it to run the calculations. I checked it too: everything lines up, and three different points really do produce the same result.
If nobody finds a hidden flaw in the formula, this will be the biggest mathematical discovery ever made with the help of an LLM.