A platform for hamburgers. Think GrubHub. In this note, we’ll try to understand what is a platform, and whether they can be improved with a “coop” structure.…

There’s a famous dubious argument that “proves” the set of $\mathrm{Tree}$ of (planar, rooted) binary trees is in bijection with the set of $7$-tuples of trees $\mathrm{Tree}^6$.…

I’ve often heard people say that the interesting part of number theory is the interaction between addition and multiplication, but I only yesterday realized one reason why that is, triggered by convincing myself that $a b = \mathrm{lcm}(a,b)\mathrm{gcd}(a,b)$ (a train of thought triggered by seeing the letters “GCD” graffitied on a wall in Chicago).…

The other day I was sitting in The Coop in Cambridge, reading a book on combinatorial games, and so naturally I started wondering about games played in groups, or on their Cayley graphs at least.…

If I say the word “swimming” to you, you’ve got a fair bit of information about what word I’m going to say next.…