Yesterday I had a great conversation with Dmitri Tymoczko about groupoids in music theory. But at this Higgs Centre Colloquium, he preferred to downplay groupoids and talk in a way physicists would ...

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 ...

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 ...

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 ...

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 ...

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 ...

Many of you have heard murmurings about this book for several months now. I’m happy to report that it’s now out! Homotopy type theory: univalent foundations of mathematics, by the Univalent ...

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 ...

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 ...

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 ...