Earlier quoted context omitted.
And yet Mathematica is not nearly as effective as math when done by pencil, paper, and a trained mathematician. The value of maths is 1) it's "open-source", 2) it's free to use, 3) if you want to switch from one module to another (say, number theory to category theory) you are able to do so using the same tools (pencil, paper, and a trained mathematician), and so long as the two "modules" are inter-operable it flows…
I should have said: "And yet Mathematica is not nearly as effective as math when done by pencil, paper, and a trained mathematician." I wasn't meaning to imply that Mathematica has no value or has little value. It's indeed awesome both productivity wise and for just enjoying the exercise of doing math. I was trying, and doing a poor job, to give reasons why pencil and paper has value. Not to the exclusion of Mathemat…
I think the interesting product idea here would be something I've never seen: a canvas on a tablet that acts like pencil and paper (drawing) but also "helps" by recognizing what you write, converting it to a formal language, and validating/verifying it. sort of the mathematica notebook, but more like a notepad