The poet Blake wrote that you can see a world in a grain of sand. But even better, you can see a universe in an atom!

Getting to the bottom of Noether’s theorem.

Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are ...

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.

Hello [email protected]. 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, ...

You may recall Greg Egan’s plea to save the magazine New Scientist from a rising tide of crackpottery after it published a glowing article about a propulsion system called the EmDrive. According to ...

Joseph Goguen, A categorical manifesto, Mathematical Structures in Computer Science 1 (1991), 49-67. Abstract: This paper tries to explain why and how category theory is useful in computing science, ...

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 ...

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 ...

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 ...

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 ...