Musical notation can actually get really hairy even when restricting yourself to pre-20th century conventions. Another notation product currently in development has a very interesting blog that delves into some of these issues (http://blog.steinberg.net/ ).

Math, on the other hand, is actually way easier even including things like mapping diagrams.

Not if you restrict the input to LaTeX notation.

Then I wouldn't see an advantage of typing on a screen vs drawing.

I have no idea what you mean.

Meaning, your recognition engine only has to recognize "\int", not ∫.

But you would never want to use a stylus to write '\int' you would want to write '∫'