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 ...

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 ...

Guest post by Utku Boduroğlu, Drew McNeely, and Nico Wittrock When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability ...

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, ...

Operads, algebras and internal algebras Let P be an operad in Set. I’ll keep it open as to whether P is symmetric or not. It makes sense to talk about P -algebras in any category with finite products, ...

Trivial examples If μ ^ is the mean value of n uncorrelated individuals, then the effective sample size is n. If μ ^ is the mean value of n extremely highly correlated individuals, then the variance ...

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 ...

These are some lecture notes for a 4 1 2 -hour minicourse I’m teaching at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. To save time, I am ...

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 ...