Here’s a recently posted TED talk by Conrad Wolfram, of Wolfram Research and wolframalpha.com. I was hopeful about this talk, because I find great entertainment value in wolframalpha.com. I was a bit disappointed. I disagree pretty strongly with what he says, even though he makes a few good points. Math, in my opinion, is not at all about solving real world problems. It’s about formal systems that express relationships between “meaningless marks on paper” (Hilbert). And to quote Poincare, “The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.” Indeed. Math is beautiful and fun. The way Mr. Wolfram presents math doesn’t sound like very much fun to me.
Random Walks
Mr. Chase blogs about math
Random Walks 
I agree, I found the message of this TED talk to be a bit nauseating. Yes, math should be relevant, and I am concerned at the notion that ‘good old-fashioned’ skills and mechanics are regarded as irrelevant preparation. I think that math without computers is all the more important now. In a society increasingly dependent on computers, is it not of critical importance to show children that their own brains can reason and compute and be creative and experience certainty?
I agree with you that messy applications aren’t beautiful, and I like how the ex-president of the MAA, Lynn Arthur Stein, defines math: the science of patterns. Math is at its core about beauty and creativity, I agree.
I also see that Conrad Wolfram has an axe to grind, working for a company that makes mathematical software. Wolfram does not dismiss creativity. He says that it comes in students doing computer programming.
However, integration by trig substitutions or by partial fractions is ugly. One of my profs used to call it “obscene” math, which is to say math that should never be done in public.
Usually beautiful math comes first, and then only later–sometimes centuries later–the applications are noted. One needs only to think of complex numbers, non-Euclidean geometry, or symmetries among the roots of polynomials to see that. There are exceptions. (Dirac’s delta function used in Physics before grounded in the theory of distributions comes to mind.)
However, one must consider Wolfram’s audience: people who are movers and shakers who might be hard-pressed to justify Federal funding of “beauty.” Even “pure research” (which uses applied math) has difficulties in being funded.
When Wolfram relegates the beauty and creativity of mathematical thinking to computer programming, he is missing one locus of creativity, visual geometric thinking.
But Wolfram might argue that manipulating geometric models beats calculation. It’s easier to see how the golden ratio and 72 degrees are related by paper folding than by calculation. (For which see
http://en.wikipedia.org/wiki/Pentagon#Simple_method and
http://en.wikipedia.org/wiki/Golden_ratio#Pentagram taken together.)
I think that was what he was starting to hint at when he closed with manipulations of a smiling stick figure.
Even beauty needs models.
Yes, I agree with what you’ve said, dad.
I think the applications of math are important, especially the things computers can do. But to exclusively emphasize these aspects of math is a mistake, in my opinion. I sense that’s what Wolfram is suggesting.
This is just to register automatic follow-up, which I forgot to do.