Chris Grossack (she/they)

It's funny how much mathematical understanding comes from just sitting with ideas for a few years.

A younger grad student asked me recently why he should care about derived categories, how he should think about them, and if I have any good resources for learning about them...

And like, I đť‘źđť‘’đť‘šđť‘’đť‘šđť‘Źđť‘’đť‘ź being there a few years ago. I remember looking for reasons to care, and wondering how to work with them and think about them, and I remember wanting good references for learning about them. And what's funny is that I was actually anticipated this! I have a LOT of really detailed notes from that time of my life because I wanted to have resources on hand for the day someone inevitably asked me this.

But looking back at them? I really don't think any of them did it for me! I think I just read dozens of papers that use derived categories freely and eventually stopped being scared. I really think the best advice is to read whatever looks interesting over many years, but it sucks because I know I would have hated that advice, haha.

Anyways, I'm sure older mathematicians will read this and think I'm young for only now having this experience, haha. But that's fine! I love smiling wistfully at younger mathematicians, and hopefully some of you older folks get the same feeling from posts like this ^_^

Mar 8 at 12:25amWeb
Show threadC.B. AberléMar 8
@hallasurvivor “in mathematics you don’t understand things, you just get used to them.”—Von Neumann
Show threadStuart PresnellMar 8

@hallasurvivor
I guess part of this experience is just letting the thing find a place in your web of mathematical concepts. You build up strands of “Oh, they’re an example of…” and “They’re useful for…” and so on, and it starts to feel a bit less alien

And as your web becomes broader and denser there are more points for the new idea to hook into. And then perhaps the new concept helps to scaffold together two ideas that seemed unrelated, and it feels like a natural part of the landscape

Show threadPhilippa CowderoyMar 8
@hallasurvivor This is the grind. Good news is you don't have to kill monsters or fight other people on the regular...
Show threadSimon BurtonMar 8
@hallasurvivor i really think this is what von Neumann meant when he was talking about "getting used to" ideas in mathematics... it's like getting used to the streets in a new town you just moved to, versus asking for directions and getting horribly confused.