The cultured mathematician?

David Brooks makes a powerful point in today's NYT: when it comes to getting smarter, books are better than the internet. (Well, I oversimplify, but go with me a moment here.)

He references Joseph Epstein's "Narcissus Leaves the Pool," which I duly referenced and read the relevant excerpt of. (Do. It's worth seeking out, and it'll take you only ten minutes.) The nut of it: a cultured person -- an ideal to which we should all aspire -- recognizes that the brain is very much finite, and so he or she focuses not on knowing as much as possible, but rather on knowing what to know, and consequently -- I love this next part -- what to forget. Finally! A cure for information overload, all without sacrificing one's love of knowledge.

Easier said than done, yes, but hey, at least the goal has a name now.

But I couldn't help thinking that that is in a real sense what I already do, at least when it comes to passing mathematical thinking to a few members of the next generation. Sure, as I've mentioned here before, I love pop culture math books. The best give a layman (including me; I'm a professional teacher but an amateur mathematician) a solid understanding of, and even intuition for, some area of math that anyone can find fascinating. But if I were to have to name a bible, a single book that informs my approach more than any other, I'd have to name Polya's "How To Solve It," because the core message and method of that book is not to know more stuff, but rather to use what you have as efficiently as possible.

And indeed it has the ring of truth, doesn't it? To lead a better life, be a better thinker. And to be a better thinker, don't seek to know more. Seek instead to make the best use of what you have.