Dec 18, 2012 Expository paper on set theory done categorically. The Modularity Theorem as a Bijection of Sets Apr 19, 2024 Bruce Bartlett floats a version of the Modularity Theorem for elliptic curves ...

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 ...

I have been looking for examples, accessible to a lay audience, to illustrate the prevalence of cohomology. Here are some possibilities: ...

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, ...

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 ...

On a scale of 0 to 10, how much does the average citizen of the Republic of Elbonia trust the president? You’re conducting a survey to find out, and you’ve calculated that in order to get the ...

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 ...

Category theory has an excellent track record of formalizing intuitive statements of the form “this is the canonical such and such”. It has been especially effective in topology and algebra. But what ...

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 ...

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 ...

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 — ...

Things equal to the same thing are also equal to one another. And if equal things are added to equal things then the wholes are equal. And if equal things are subtracted from equal things then the ...