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 ...

Hello unknown@52.167.144.225. So nice of you to stop by. I'm a member of the Theory Group here at UT. I've been at UT since September 1994. Before coming here, I was an Assistant Professor in 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, ...

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 ...

Jun 13, 2026 A new characterization of the Standard Model gauge group as the group of symmetries of an octonionic qutrit that restrict to act as unitary operators on an ordinary qutrit and, within ...

I mentioned in my intro that as wonderful as n n-categories are, they’re really just one (important) part of the zoo of “higher categorical structures” out there. Today I want to tell you about ...

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 ...

I’ve been blogging a bit about medieval math, physics and astronomy over on Azimuth. I’ve been writing about medieval attempts to improve Aristotle’s theory that velocity is proportional to force, ...

Then K K is the category of substructures of a countable structure M M which is universal and homogeneous. Examples include the Rado graph as the Fraïssé limit of the category of finite graphs and ...

David Corfield likes theorems that say what’s special about the real numbers — especially theorems where ℝ \mathbb{R} emerges unexpectedly at the end, like a rabbit from a magician’s hat. He enjoys ...

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 ...

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 ...