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 ...

Freeman Dyson is a famous physicist who has also dabbled in number theory quite productively. If some random dude said the Riemann Hypothesis was connected to quasicrystals, I’d probably dismiss him ...

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 ...

I want to talk about some attempts to connect the Standard Model of particle physics to the octonions. I should start out by saying I don’t have any big agenda here. It’d be great if the octonions — ...

Summer saw the foundations of mathematics rocked by the publication of The HoTT Book. Here we are a few months later and the same has happened to physics with the appearance on the ArXiv of Urs’s ...

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 ...

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 ...

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 ...

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 ...

such that the following 5 5 diagrams commute: (for f: x 0 → x 1 f:x_0\to x_1 and y ∈ 풞 y\in\mathcal{C}, we write f ⊗ y f\otimes y to mean f ⊗ id y: x 0 ⊗ y → x 1 ⊗ y f\otimes\operatorname{id}_y: ...

I’m in Regensburg this week attending a workshop on Interactions of Proof Assistants and Mathematics. One of the lecture series is being given by John Harrison, a Senior Principal Applied Scientist in ...

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 ...