I should have said: "And yet Mathematica is <sometimes> 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 Mathematica or more so than Mathematica. Just, that it still has tons of value. And that, maybe that is what these open source projects are trying to recreate that Mathematica has not yet captured.