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 ...

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.

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 ...

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, ...

The notion of Cohesive Topos The definition of cohesive topos or category of cohesion aims to axiomatize properties of a topos that make it a gros topos of spaces inside of which geometry may take ...

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 ...

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 ...

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

I think I’m gradually coming to understand why some people think (∞, 1) -toposes are the best thing since sliced bread. For me, I think a brief way to describe what’s so amazing about them is that ...

Outline of this blog Throughout this blog post, we will present many of the ideas in the paper “String Diagrams for lambda calculi and Functional Computation” by Dan R. Ghica and Fabio Zanasi from ...

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 ...