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 ...

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, ...

But for some reason I’ve never studied crossed homomorphisms, so I don’t see how they’re connected to topology… or anything else. Well, that’s not completely true. Gille and Szamuely introduce them ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

You probably know that the 2010 Fields Medals have been announced. The thing is, I’ve never succeeded in understanding the slightest thing about it. It’s as if it’s got a hard, shiny shell—it resists ...

A Yoneda structure on a 2-category consists of two pieces of data satisfying three axioms. We will see that the data is what is necessary to naturally express the Yoneda lemma in the 2-category, and ...

It’s an underappreciated fact that the interior of every simplex Δ n \Delta^n is a real vector space in a natural way. For instance, here’s the 2-simplex with twelve of its 1-dimensional linear ...