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 which gets at the Standard Model gauge group and its representation on one generation of fermions starting from a Jordan triple ...

Dec 31, 2014 Mumford’s obituary of Grothendieck was rejected by Nature. This Week’s Finds in Mathematical Physics (Week 281) Oct 20, 2009 In “week281” of This Week’s Finds, learn about the newly ...

Bless British trains. A two-hour delay with nothing to occupy me provided the perfect opportunity to figure out the relationships between some of the results that John, Tobias and I have come up with ...

such that the following 5 5 diagrams commute: (for f: x 0 → x 1 f:x_0\to x_1 and y ∈ 풞 y\in\mathcal{C}, we write f ⊗ y f\otimes y to mean f ⊗ id y: x 0 ⊗ y → x 1 ⊗ y f\otimes\operatorname{id}_y: ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...

I don’t know much about continued fractions yet, so it’s too early to be describing historical phases of work on the subject, but I can’t resist doing it. I’ll talk about three: By thinking about ...

I’m in Regensburg this week attending a workshop on Interactions of Proof Assistants and Mathematics. One of the lecture series is being given by John Harrison, a Senior Principal Applied Scientist in ...

John Baez, Joe Moeller and Todd Trimble, Schur functors and categorified plethysm. This paper has been 14 years in the making. So let me tell you a bit of its history, and then I’ll explain the paper ...

Over the last few years, I’ve been very slowly working up a short expository paper — requiring no knowledge of categories — on set theory done categorically. It’s now progressed to the stage where I’d ...

Last time I reviewed a bit of Bott periodicity. Now I want to start leading up to a question about it. It will take a while. So, this time, I will explain a wonderful one-to-one correspondence between ...