It’s long been a mystery why there are 3 generations of quarks and leptons: three sets of particles, apparently identical except for how they interact with the Higgs boson. It would be nice if there ...

Aug 17, 2026 How you can fit the Lie algebra of the Standard Model gauge group and its representation on three generations of fermions into the Lie algebra of E7.

Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are ...

This is the first of a series of posts on how large cardinals look in categorical set theory. My primary interest is not actually in large cardinals themselves. What I’m really interested in is ...

The following is the greatest math talk I’ve ever watched! Etienne Ghys (with pictures and videos by Jos Leys), Knots and Dynamics, ICM Madrid 2006. [See below the fold for some links.] I wasn’t ...

Back to modal HoTT. If what was considered last time were all, one would wonder what the fuss was about. Now, there’s much that needs to be said about type dependency, types as propositions, sets, ...

But for some reason I’ve never studied crossed homomorphisms, so I don’t see how they’re connected to topology… or anything else. Well, that’s not completely true. Gille and Szamuely introduce them ...

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 don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to learn, only to have my ...

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 ...

Freeman Dyson is a famous physicist who has also dabbled in number theory quite productively. If some random dude said the Riemann Hypothesis was connected to quasicrystals, I’d probably dismiss him ...

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 ...