By combining scientific world models and mathematical proofs we will aim to construct a ‘gatekeeper’, an AI system tasked with understanding and reducing the risks of other AI agents. In doing so ...

Today I heard from David Benson that Jack Morava died yesterday. This comes as such a huge shock that I can’t help but hope Benson was somehow misinformed. Morava has been posting comments to the ...

August 2025's Entries (BT) Diversity from (LC) Diversity Jack Morava Random Past Entries TeXnical Issues Sage advice on viewing this blog and posting comments thereon. Categories, Logic and Physics in ...

Announcing the Clowder Project: a wiki and reference work for category theory built using the same general infrastructure and tag system of the Stacks Project.

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, ...

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’m a little bemused by the popularity of the Galois theory notes. I’ve made quite a few sets of course notes public before, e.g.: Fourier analysis General topology Linear algebra Category theory But ...

Posted by John Baez I keep wanting to understand Bernoulli numbers more deeply, and people keep telling me stuff that’s fancy when I want to understand things simply. But let me try again. The ...

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 ...

Why Mathematics is Boring 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 ...

In this year’s edition of the Adjoint School we covered the paper Triangulations, orientals, and skew monoidal categories by Stephen Lack and Ross Street, in which the authors construct a concrete ...

Despite the “2” in the title, you can follow this post without having read part 1. The whole point is to sneak up on the metricky, analysisy stuff about potential functions from a categorical angle, ...