To draw these graphs we need to use Riemann’s explicit formula for π (x) \pi (x) as a sum over zeros of the Riemann zeta function. My calculations use twice as many zeros as Bays and Hudson had access ...

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 ...

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 ...

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 learn, only to have my ...

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, ...

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 ...

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 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 ...

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: ...

It builds on things I’ve discussed here, but it goes further. Let me explain a bit. A bit is just a binary alternative: 1 or 0, true or false. That’s how it works in classical logic. We could also ...

Over the last few years, I’ve been very slowly working up a short expository paper — requiring no knowledge of categories — on set theory done categorically. It’s now progressed to the stage where I’d ...

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 ...