Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are ...

Note: These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older ...

How do you count rooted planar n -ary trees with some number of leaves? For n = 2 this puzzle leads to the Catalan numbers. These are so fascinating that the combinatorist Richard Stanley wrote a ...

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, ...

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 ...

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 ...

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 ...

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 ...

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, ...

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 ...

The Notices of the AMS has just published the second in its series “Mathematicians discuss the Snowden revelations”. (The first was here.) The introduction to the second article cites this blog for “a ...

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 ...