Spent the last week or so watching videos from Michael Starbird, math professor at University of Texas Austin. Guy is good at what he does, if you have any interest in it. Probably better for high school through college students, those that just want a refresher on material, those who want to apply this stuff to their line of work or living, or parents who want to help their kids at school. Probably not all that great if you are someone who is younger than 14 or 15 and isn't interested in the material on your own, or are overly familiar with the material. Which is to say, perfect for me.
The videos are produced by The Teaching Company. I'm not sure, but I get the impression they distribute videos nationwide. You might be able to find some of these at your local library, if interested. I might have more to say on Starbird and his videos later. Might not.
I think one of the most interesting things is the way he described how professionals like him see beauty in proofs. The beauty of proofs, says Starbird, comes from when you find unexpected, unintended truths that very simply describe previously unseen complexities. His thinking comes together, in one, when he visually describes the proof behind the existence of the 9-point circle on any triangle (Mathematics From The Visual World, Chapter 5, 16:00).
The proof itself is something I couldn't redo or completely understand if you asked me. But what strikes me is how much his description of aesthetic beauty in proofs reminds me of art. Music in particular.
You take a bunch of stuff that simply is, mess around with it, put it all together in some order, and "prove" or show (really, come across) something unexpected that holds some sort of universal aesthetic or truth. And that unexpected, unique property just draws people back time and time again. That actual proof may just be a happy accident. And it often is. But it comes from things that are very real, things that you learn from just being in it, and playing with the material, so to speak. You get there doing, exploring, experiencing. It sounds so... yes.
My ears are open.