If you want good ideas for revolutionising mathematics education, you picked the wrong TED talk. Summary of Wolfram's talk: we still teach people maths as if we were living 50 years ago, when the ability to actually do this stuff on paper was useful. It would be much more sensible to be teaching them how to use computers optimally, as that's what people who use maths in real life actually do.
My summary of Wolfram's talk (which he might not endorse): if it's a choice between teaching people maths and teaching them programming, teach them programming.
Speaking of Wolfram, I learned calculus (in my freshman year of college) in a then-new, Mathematica-based course called Calculus & Mathematica. (My backwoods high school had no pre-calc or calculus).
I really liked it; we were freed of the boring mechanical stuff, leaving time to better learn the underlying concepts. There were plenty of examples that non-programmer-types could copy, paste and tweak. (As a side effect, the then-shiny, new NeXTStations got me interested in then-new Linux).
It seems to still be going today, though I've not kept up with the people.
This guy says that the problem is that high-school math education is structured to prepare people to learn calculus in their freshman year of college. But only a small minority of students ever takes calculus, and an even smaller minority ever uses it. And not many people ever make much use of pre-calc subjects like algebra, trig, or analytic geometry.
Instead, high-school math should be structured to prepare people to learn statistics. Probability and basic statistics, he argues, are not only more generally useful than calculus, they are also more fun.
I have to agree with him. What do the people here think?