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 ...

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 ...

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, ...

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 ...

an appreciation of Bill Lawvere’s work in this direction. More is behind the above link. The idea behind the term is that a geometric space is roughly something consisting of points or pieces that are ...

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 ...

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 ...

This semester I’ve been teaching an undergraduate course on Galois theory. It was all online, which meant a lot of work, but it was also a lot of fun: the students were great, and I got to know them ...

Faster-than-light neutrinos? Boring… let’s see something really revolutionary. Edward Nelson, a math professor at Princeton, is writing a book called Elements in which he claims to prove the ...

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 ...

Of course this is an odd question. Since the octonions are nonassociative you might fear the map ...

These are notes for the talk I’m giving at the Edinburgh Category Theory Seminar this Wednesday, based on work with Joe Moeller and Todd Trimble. (No, the talk will not be recorded.) They still have ...