I take notes in LaTeX, using EMACS. I find I can keep up with any math class. Diagrams are a problem, so what I do is keep a composition book for supplementary material. Then, on my LaTeX notes I can say "see sketch 1 in composition book, 7 Feb 2010." But, you need to use trial and error, find what works for you, and do that. I find if I take notes by hand, I run the risk of falling asleep. LaTeXing the notes is fun, produces a good finished product, plus I check the .tex into SVN and one of my colleagues will compare against his handwritten notes and make corrections. Plus, I would lose things that aren't version controlled, including most of my handwritten notes :)

1) Learn Emacs
2) Learn the AucTeX shortcuts
3) AucTeX has a mode called latex-math-mode. This gives you quick shortcuts for entering the Greek letters and some common set notation
4) Create your own Emacs macros
5) Create your own LaTeX commands

For example:
\newcommand\probspace{(\Omega, \mathcal{F}, \mathbb{P})}
will be helpful if you are taking notes in probability.

I have used this combination of tools and I can take notes in real-time in most math classes.

The IBM T221 would work. T221

Already Exists

Tex the world http://thewe.net/tex/

> very possible TeX does an awful lot more than that.

Very possible? I would say more like established fact. For example, can you embed R code in a Word document to produce research papers such that exact code that generated every number, chart, and table in the paper is in the same document as the writeup (reproducible research). You can with LaTeX with Sweave ( http://www.stat.umn.edu/~charlie/Sweave/ ).

And that is one of MANY things LaTeX can do that Word cannot.

Care to post the list? That would be quite helpful for me and others as well.