This is astounding. Gilles Castel uses LaTeX to take notes in his Math classes. These aren’t simple notes with a smattering of elementary math symbols; they’re notes for classes like Complex Variables and other advanced topics. Take a look at his post for some examples.
I say it’s astounding because I wouldn’t have believed you could type the LaTeX fast enough to keep up with the instructor. Castel’s goal is to be able to type the LaTeX as fast as the instructor could write the mathematics on the board. To make this possible, Castel uses UltiSnips snippets and Vim. He’s got a number of custom snippets—some quite complicated—that intelligently expand to LaTeX and enable him to enter the mathematics at speed.
Naturally, I started wondering how his procedures would port to Emacs and AUCTeX. I’ve never used UltiSnips but it seems similar to yasnippet except for supporting regular expressions in the keys. On the other hand, AUCTeX provides a lot of functionality that Castel implements with snippets. The post contains several animated GIFs that show how his system works in practice. Watch them and be amazed. If you’re an UltiSnips user, Castel’s snippets are available here for you to try.
Regardless of which editor and snippet package you use, I’d guess that it’s going to take some concentrated practice to get fast enough to actually use in class.