John C. Baez

johncarlosbaez.bsky.social

23 July 2026 20:07

Alpöge's counterexample to the Jacobian conjecture has consequences for quantum mechanics in 3 dimensions! You can find operators obeying the usual position–momentum commutation relations that generate a smaller algebra than the usual ones do. Some observables become unreachable. (1/9)

John C. Baez

johncarlosbaez.bsky.social

23 July 2026 20:07

In 1968, the famous mathematician Jacques Dixmier conjectured that every endomorphism of W₃ is an automorphism: basically, you can't squoosh the algebra into smaller piece of itself. But the new counterexample to the Jacobian conjecture shows you CAN! (3/9)

John C. Baez

johncarlosbaez.bsky.social

21 July 2026 08:36

The Gaussian Moments Conjecture is a pretty conjecture connected to probability and quantum field theory. Two days ago we suddenly learned it's false! - since it implies the Jacobian conjecture. Let me explain this conjecture - it's pretty simple as these things go. (1/n)

Nereide

drnereide.bsky.social

18 July 2026 05:16

1/12 John Baez et al. have just published a paper linking decades-old #mathematics to a new way of thinking about quantum mechanics. 🔭🧪⚛️ The result? The Standard Model (SM) of particles seems to emerge naturally from certain mathematical structures. Here’s a simple explanation, I hope. #physics

John C. Baez

johncarlosbaez.bsky.social

08 July 2026 06:50

He's back. And you can see he's not taking any more of this shit.