Why isn't there a good way of doing symbolic math on a computer?

I want to brush up on my probability theory. I hate using a pen and paper, I lose them, they get damaged, and my handwriting is slow and messy.

In my mind I can envisage a simple symbolic math editor with keyboard shortcuts for common symbols, that would allow you to edit nice, neat latex style equations, as easily as I can edit text. Markdown would be acceptable as long as I can see the equation in it's pretty form next to it. This doesn't seem to exist. Python based symbolic math systems, like 'sagemath', are hopelessly clunky. Mathematica, although I can't afford it, doesn't seem to be what I want either. I want to be able to write math fast, to aid my thinking while proving theorems and doing problems from a textbook, not have the computer do the thinking for me. Latex equation editors I've seen are all similarly unwieldy - waiting 10 seconds for it to build the pdf document is totally disruptive to my thought process.

Why isn't this a solved problem? Is it just that nobody does this kind of thing on a computer? Do I have to overcome my hatred of dead tree media and buy a pencil sharpener?