Dec 7, 2025 There are two ways to stick SU(2) × SU(3) in Spin(10). One is good for physics; the other, alas, is easily obtained using the octonions.

Define the Standard Model gauge group to be S ( U ( 2) × U ( 3)), the subgroup of SU ( 5) consisting of block diagonal matrices with a 2 × 2 block and then a 3 × 3 block. (This is isomorphic to 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 ...

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, ...

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 ...

Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional Distributional Model of Meaning, by Bob Coecke ...

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 ...

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 ...

The study of monoidal categories and their applications is an essential part of the research and applications of category theory. However, on occasion the coherence conditions of these categories ...

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 ...

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 ...