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 ...

A light mill is also known as a Crookes radiometer: It seems like a simple thing: an evacuated glass bulb with some vanes that can spin around, black on one side and white on the other. When you shine ...

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 ...

Nine short stories about geometric higher categories. Today, I only want to focus on two basic questions about geometric higher categories: namely, what is the idea behind the connection of geometry ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

Part of what intrigues me about reading Terence Tao’s blog is that he displays there a different aesthetic to the one largely admired here. The best effort to capture this difference is, I believe, ...

The study of monoidal categories and their applications is an essential part of the research and applications of category theory. However, on occasion the coherence conditions of these categories ...

There’s been a bunch of discussion online recently (e.g. SBS, MathOverflow 1, 2, 3, etc.) about set-theoretic foundations for category theory, the role of universes, and so on. So I thought I would ...

Here is a comment about the bar construction which I wanted to mention, since John told me that his course is ending soon and he might not get around to mentioning it himself. I’d like to thank Urs ...

A few of us here at the Café decided that it would be good to have a short series of posts in which each of us (at least, each of us who wants to) says something about his overall take on higher ...

A note to those arriving from the article in the Chronicle of Higher Education: my opinion may not have been accurately represented in that article. Please read my whole post and judge for yourself.

Here’s what Nick Kuhn wrote on the ALGTOP mailing list: Yesterday, at the conference on Geometry and Physics being held in Edinburgh in honor of Sir Michael Atiyah, Harvard Professor Mike Hopkins ...