2. You really don't need to know about automata theory, linear algebra or whatever to be a good developer. Brings me back to what I said in 1.
No, but all of those things (like the Fourier transform you skipped mentioning) can be used to turn difficult problems into simple ones, making you an even better developer.
Yes, but it's like a thousand other things that can make you a better developer.
It has always seemed quite useless to me to try to learn as much theory as you can before starting to actually do significant projects. You should learn by doing those project, and when it appears that you need theory to make it better, then you learn it.
I think there is a huge parallel with the lean model for CS teaching, programming yourself should always be the starting point.
It has always seemed quite useless to me to try to learn as much theory as you can before starting to actually do significant projects.
I agree with this, but I also advocate occasionally exploring random theory that's unrelated to your current projects, expanding your mental toolbox. Sometimes you don't know you have a problem until you've already heard of the solution.
No, but all of those things (like the Fourier transform you skipped mentioning) can be used to turn difficult problems into simple ones, making you an even better developer.