As part of their big theorem dump, an AI company recently emitted a proof of the ‘quasi-Riemann hypothesis’. Maksym Radziwiłł of New York University said the implications of this result are ...

Jan 9, 2008 On the notion of topos-theoretic quantum state objects, the proposed definition by Isham and Doering and a proposal for a simplified modification for the class of theories given by charged ...

Sep 10, 2014 Guest post by Bruce Bartlett I recently put an article on the arXiv: Bruce Bartlett, Quasistrict symmetric monoidal 2-categories via wire diagrams. It’s about Chris Schommer-Pries’s ...

and he okayed me posting them here. He’s taking the idea of categorifying the Riemann zeta function, explained in my paper, and going further, imagining what it might mean to categorify Riemann’s ...

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 ...

such that the following 5 5 diagrams commute: (for f: x 0 → x 1 f:x_0\to x_1 and y ∈ 풞 y\in\mathcal{C}, we write f ⊗ y f\otimes y to mean f ⊗ id y: x 0 ⊗ y → x 1 ⊗ y f\otimes\operatorname{id}_y: ...

Let’s climb up to the E 6 root polytope starting with some of its 4-dimensional faces, which are called 4-demicubes because you get them by taking a 4-dimensional cube, or tesseract, and removing ...

The previous post introduced the plumbing calculus: typed channels, structural morphisms, two forms of composition, and agents as stateful morphisms with a protocol for managing their state. The ...

Bless British trains. A two-hour delay with nothing to occupy me provided the perfect opportunity to figure out the relationships between some of the results that John, Tobias and I have come up with ...

These seven equations between binomial coefficients are ‘coincidences’ — they aren’t among the four known infinite families of such equations: At that time, he and his collaborators checked there were ...

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 — ...

Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional Distributional Model of Meaning, by Bob Coecke ...