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Basically it's a front-end to LaTeX. You can export various formats from it, and PanDoc allows one to get to pretty much anything.

I use it on a small tablet PC and it allows handwriting input.

If I need a math equation I write it out in Infty Editor: http://www.inftyproject.org/en... and paste in the LaTeX code.

If I need a diagram, I draw it up in Corel Grafigo, InkScape, Macromedia Freehand, or Dia and include it as a .pdf

Software already available for that (has been since Instant TeX on a NeXT though that only did single characters):

InftyEditor - http://www.inftyproject.org/en/software.html

FFES - http://research.cs.queensu.ca/drl/ffes/

There's also

MathJournal - http://www.xthink.com/MathJournal.html

which is a commercial product, the new version supports LaTeX

William

I used Infty Editor in my classes - I think it's based on LaTeX but, it was pretty quick. I didn't use it to take notes in realtime though, so I can't tell you how successful that would be. http://www.inftyproject.org/en/software.html

InftyReader is a program that specializes in doing OCR on scientific documents and mathematical formulas. It saves documents in a variety of formats including LaTeX and MathML.

Two unfortunate things about it: 1) it's a Windows binary 2) it costs $900USD for 2 concurrent use licenses. It was free until they licensed a conventional OCR engine to better handle the text (its non-math recognition was pretty bad before).

Once you're there, understanding that z^2 = x^2 + y^2 is equivalent to a^2 + b^2 = c^2 is easy.

What I'm saying is that's the tough part, whereas the OCR is comparatively easy (eg InftyReader).

You can only transform an equation if you know its meaning (ie the rules of transformation embodied by the context in which it is being written). And understanding the meaning is a hard AI problem.

I wouldn't say so, check http://www.inftyproject.org/ Their OCR claims 99% success in printed documents (i've tried it is true). And wait a few years,there are some really promising papers out there, i bet you'll be amazed on the number of people working on this problem since the late 90's. 3 years from now i am almost sure you'll be able to enter any kind of math expression by hand using a digitizer (don't ask handwritten offline OCR just yet though :( )
check out this guy as well http://www.cs.berkeley.edu/~fateman/ his work is groundbraking, i hope they will have a solid opensource system in a couple of years

The only one I'm aware of is FFES (Freehand Formula Entry System)

http://freshmeat.net/projects/ffes/

Not opensource AFAICT is Infty:

http://www.inftyproject.org/en/

William