: New: Book Report: The Best Writing in Mathematics 2012

This was a mixed bag. The good news is that not all the writing in this collection is aimed at mathematicians, since I'm not a mathematician. The bad news is that a bunch of math writing for non-mathematicians is philosophy about the purpose of math: is the coolest math that which relates to the real world or that which is totally abstract? Whether or not you believe that math should be "useful" I think we can all agree that arguing about the utility of math is not useful. Where by "we... all" I mean everyone except the folks who wrote essays about this that made it into this book.
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There were some essays that were over my head. If I'd been willing to buckle down and learn quaternions, this would have been my chance. But I'm pretty happy to let other folks write the 3-D graphics libraries so that I can ride on their coattails. I kind of followed a description of Vinogradov's theorem, which was fun. There was an essay about how to create pretty origami "weaves" that I almost skipped because the beginning was trying so hard to be abstract-mathy instead of saying "Hey we're trying to figure out ways to fold paper to make things that look like this". Still, I think the main thing that I got out of this book was some recommended-reading in the editor's introduction; a couple of books too long to fit in this collection of essays, but which I might be able to understand.

Erica Flapan had a darned good essay about teaching, How to Be a Good Teacher Is an Undecidable Problem. Don't expect folks to publicize it too widely, though. It doesn't have some new breakthrough to tell you. It's more of a history of someone who's tried using some of those "breakthroughs" in the classroom: some of them worked, some of them didn't, personal style probably determined which worked best. So try new things, stay interested, but don't expect that cool technique that you read about in that magazine to change everything. So darned sensible that you shouldn't even have to point it out, but you know, people get excited about things breathlessly reported upon in magazines. (Fun fact: this essay collection costs less than this essay on its own as sold by JSTOR. Which tells you something about the state of academic publishing nowadays; but probably not anything you didn't already know.)

There was an interesting biographlet of Augustus De Morgan, concentrating on his mentoring activities. Remember, kids, individual accomplishment is all very well and good. But if you wish to be remembered well in history, that's not enough. It's good to mentor some folks who go on to do great things and who remember you fondly when folks are looking for quotes. (There are also some altruistic reasons to mentor folks, but if you're motivated by those then you probably don't need stories from the live of De Morgan to inspire you.)

There was an essay about the Traveling Salesman Problem and other routing problems that have popped up in history and modern times. It was fun, though it's pretty much all leaked out of my head again in the time since I read it.

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