indeed!!

one of the things I've never liked about algebraic topology is how much one you seem to compute hard crunchy things (e.g. homology groups) by drawing loopy pictures. in probability it feels like you tend to understand what's visually going on with hard syntactic calculation, which I much prefer

I love this, I also think of nilpotents as "thick" points

yeah seems like a wildly bad heuristic, especially when the "good at math" level here is pre-k math...

"semi-mature" is really pushing it

I would rather whip cream by hand and give myself carpal tunnel (speaking from experience) than buy cool whip

I guess for us, the prototypical graphs are like Z^d, complete graphs on n vertices, or maybe a k-regular trees, perhaps the most boring graphs possible from a graph-theoretic perspective!

oh I very much feel this, as a probabilist I don't have the same conception of graphs that a finite graph theorist does at all, clearly. the most I would really think about is if a graph is bipartite. there's some intersection certainly, but I'm never thinking about like, Ramsey numbers

(he was thinking about d-dimensional hyperbolic space or something if I recall correctly and there's some relevant algebra there)

definitely feel this as a probabilist. was talking with one of the best percolation theorists in the world and he told me about a proud moment at a conference recently where he wrote down a short exact sequence for the first time. lol