Just a mathematical meditation for today...:
About 10 days ago in a longish post over at MathTango I included some links to Keith Devlin materials -- one of my favorites was a podcast he did for NPR's "On Being," an always-wonderful radio-hour. In that conversation he made the following observation, which I fancy, regarding a transition on the road to becoming a mathematician [bold added]:
"...that's when I became a mathematician; that's what I stumbled on at age 15 or 16 when here I was learning all this mathematics because I needed it. I had a utilitarian view of mathematics. I was learning it because I needed to solve the equations because I was going to be solving them in physics. And then, at the age of about 16 or 17, it all fit because it all came together in my mind. It was no longer this disjointed collection of techniques you could use to solve problems. It all fell into place, into this wonderful landscape. It was as if I'd been stumbling around in a forest, and suddenly I've climbed to the top of a tree and looked out and thought, this is the most beautiful place in the world. You can't tell it when you're down in the trees, which I had been, but the moment you reach an elevation where it all falls into place and you can see the whole topographic display in front of you, then the beauty is incredible. And the moment I discovered it, I said, um, I want to study mathematics. And I've been studying it ever since."I love this imagery of most of us exploring down amongst the trees and forest floor, versus looking out above the canopies over the whole forest landscape that is mathematics. This is what Ed Frenkel essentially talks about, especially in working on the Langlands Program which brings together disparate aspects of mathematics... the separate sections of the forest linking together when we zoom out far enough. The same idea comes up in discussions of symmetry, group theory, number theory, and other areas of math, unlike the more disjointed way math must often, perhaps of some necessity, be taught in the classroom. The individual trees and groves can of course be beautiful and stately all by themselves… but, ohhh, to take in that majestic view from above the treetops!!