where F n are the Fibonacci numbers 0, 1, 1, 2, 3, … and L n are the Lucas numbers 2, 1, 3, 4, 7, …. These are two sequences satisfying the same famous recurrence relation, just with different initial ...

Let’s climb up to the E 6 root polytope starting with some of its 4-dimensional faces, which are called 4-demicubes because you get them by taking a 4-dimensional cube, or tesseract, and removing ...

Last time I described a way to get the Standard Model gauge group from the exceptional Jordan algebra. But that approach gave no obvious nice way to put quarks and leptons into the picture. This new ...

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 ...

Apr 29, 2026 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 ...

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 ...

and he okayed me posting them here. He’s taking the idea of categorifying the Riemann zeta function, explained in my paper, and going further, imagining what it might mean to categorify Riemann’s ...

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, ...

In this post and the next, I want to try out a new idea and see where it leads. It goes back to where magnitude began, which was the desire to unify elementary counting formulas like the ...

We’re brought up to say that the dual concept of injection is surjection, and of course there’s a perfectly good reason for this. The monics in the category of sets are the injections, the epics are ...

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, ...

I haven’t been carefully following quantum field theory these days, but some folks on the Category Theory Community Server asked me what I thought about recent work using the ‘amplitudohedron’ and ...