Keller maps
An explicit family of counterexamples to the Jacobian conjecture in every dimension n ≥ 3, worked out with GPT-5.6 Sol. Two preprints.
I wanted to see how far I could push an AI model on real mathematics. Starting from Levent Alpöge’s example in three dimensions, I pushed GPT-5.6 Sol to find new examples that weren’t simple variations of it, and then to generalize them to a family that works in every dimension n ≥ 3.
The results are in two preprints. Terence Tao unpacked how the family works on his blog, and José A. R. Fonollosa has built on it since.