any generation of Standard Model fermions transforms as the direct sum of six irreducible representations: These correspond to the six types of left-handed fermion: q L, d R, u R, ℓ L, e R, ν R. Six ...

Jul 18, 2026 John Baez, Endre Bokor and Latham Boyle have a new paper called “Jordan pair quantum theory and the Standard Model”.

It builds on things I’ve discussed here, but it goes further. Let me explain a bit. A bit is just a binary alternative: 1 or 0, true or false. That’s how it works in classical logic. We could also ...

In the last episode of my column in Notices of the American Mathematical Society, we looked at a particle moving in an attractive central force whose strength is proportional to the inverse cube of ...

The Univalence Principle is the informal statement that equivalent mathematical structures are indistinguishable. There are various ways of making this statement formally precise, and a long history ...

Here’s a draft of my next column for the Notices of the American Mathematical Society. It’s about the inverse cube force law in classical mechanics. Newton’s Principia is famous for his investigations ...

Despite the “2” in the title, you can follow this post without having read part 1. The whole point is to sneak up on the metricky, analysisy stuff about potential functions from a categorical angle, ...

People in measure theory find it best to work with, not arbitrary measurable spaces, but certain nice ones called standard Borel spaces. I’ve used them myself. a finite or countably infinite set with ...

I’ve been blogging a bit about medieval math, physics and astronomy over on Azimuth. I’ve been writing about medieval attempts to improve Aristotle’s theory that velocity is proportional to force, ...

Sep 30, 2024 Let’s think about how classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant \(k\) approaches zero, by looking at an example.

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

I keep wanting to understand Bernoulli numbers more deeply, and people keep telling me stuff that’s fancy when I want to understand things simply. But let me try again.