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 ...

Nine short stories about geometric higher categories. Today, I only want to focus on two basic questions about geometric higher categories: namely, what is the idea behind the connection of geometry ...

My friend the combinatorist Bill Schmitt breezed through Paris recently, taking a train back from Hopf-in-Lux with Paul-André Melliès, and spending a day here before going home to DC. We had some time ...

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

Part of what intrigues me about reading Terence Tao’s blog is that he displays there a different aesthetic to the one largely admired here. The best effort to capture this difference is, I believe, ...

Whether we grow up to become category theorists or applied mathematicians, one thing that I suspect unites us all is that we were once enchanted by prime numbers. It comes as no surprise then that a ...

Nov 3, 2025 Exploiting the secret 4-dimensional symmetry of the Kepler problem to think about the periodic table of elements in a new way.

Given a particle in Euclidean space, a central force is a force that points toward or away from the origin and depends only on the particle’s distance from the origin. If the particle’s position at ...

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 ...

Last summer my students Brendan Fong and Blake Pollard visited me at the Centre for Quantum Technologies, and we figured out how to understand open continuous-time Markov chains! I think this is a ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

John Huerta’s paper on grand unified theories made some people eager to discuss aspects of group representation theory that this paper deliberately avoided. For example, in relativistic quantum ...