I’m giving a talk online tomorrow at the 2026 Spring Southeastern Sectional Meeting of the American Mathematical Society, in the Special Session on Non-Associative Rings and Algebras. The organizers ...

Example: suppose we have a data structure representing an abstract address. An address is, alternatively, an email address or a postal address like in the previous example. We can try to extract a ...

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 ...

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 ...

I have been looking for examples, accessible to a lay audience, to illustrate the prevalence of cohomology. Here are some possibilities: ...

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 ...

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 ...

It’s an underappreciated fact that the interior of every simplex Δ n \Delta^n is a real vector space in a natural way. For instance, here’s the 2-simplex with twelve of its 1-dimensional linear ...

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 previous post introduced the plumbing calculus: typed channels, structural morphisms, two forms of composition, and agents as stateful morphisms with a protocol for managing their state. The ...

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 ...

Peter Scholze has just published a challenge to the automated mathematical formalisation community in a post – Liquid tensor experiment – on Kevin Buzzard’s blog. Peter explains there the motivation ...