I just got out of a meeting with a Real Mathematician™ who's interested in my research?? He's not even in my department!!

We talked about the work I've been doing for like an hour, and he gave me some feedback on a preprint, and then invited me to give a talk on this machinery at his department??

Oh my god I can't believe someone else actually cares about the things I think about, I could cry. The people in my department have all been pretty unenthusiastic about it, so it's awesome to learn that someone else is (almost) as excited as me!

This has also been great because I've been feeling pretty down about my mathematical abilities lately. Every time I get depressed I start doubting whether I'm cut out for this (which I know is common), and I've been pretty depressed lately. This made me feel a lot better.

Also, to say a word about that, I know that I'm really good at LEARNING math, and that I know a lot of things. I also think that I'm quite good at TEACHING math, which I value really highly. My big insecurity is that I'm not actually that good at DOING math. Research is hard, but the imposter syndrome is really awful when I feel like everyone knows that there's other aspects of math that I ~am~ really good at...

I wish there were a place in the academy for people who learn hard things and then write better books and give talks and exposit, since I really think that's where my skills naturally lie. I love convincing people that hard math doesn't have to be scary.

Well, once I have tenure maybe I can do a 180 and start writing expository books. Or maybe by then I'll be less insecure about doing research and I won't want to anymore! Who's to say, haha.