Hello again, dear reader!
I haven’t written anything here in quite a while now — since February 22, it would seem! Partly, that’s because I’ve been busy visiting graduate schools and deciding where to go. And I can now happily announce that my wife and I will be moving to Philadelphia this summer, where I will begin a computer science PhD at the University of Pennsylvania in the fall. I’m super excited!
So, what does that mean for this blog? Not to worry — as of right now, I plan to continue right on with the same tasty accessible math you’ve come to (hopefully) love and (rightfully) expect! Plans can always change, of course, but right now I intend and hope to continue this blog while in grad school. Will I keep writing this blog until I die? Probably not! I’ll stop at some point, but that point isn’t here yet. =)
For now, a link: if you haven’t yet read “A Mathematician’s Lament” by Paul Lockhart — a telling and insightful lament over the current state of mathematics education in the US, which transcends the usual petty debates — I highly recommend it, whether you’re a teacher, a student, or (ideally) both! It’s both depressing and inspiring at the same time. He puts eloquent and forceful words on things I’ve thought only dimly.
The Math Less Traveled 
Awesome! Glad you’re back, and glad you’re coming to Penn! I’m finishing up undergrad here in a few weeks – I think you’ll love the program here.
Ryan: thanks! And congrats in advance on your graduation. =)
Oh whew, I was beginning to wonder if I should stop checking for updates. This one was worth the wait. I first expected it to be about fuzzy math; instead, it’s about the math classes I took.
I’m not entirely convinced that mathematics is an art. Mathematicians are discoverers more than creators, and don’t tell me that artists “discover” the statue hidden in the marble. But Lockhart’s attitude on teaching in general fits with what I’ve come to believe.
Steve: you know, if you use a newsreader (like e.g. Google Reader), or subscribe to receive updates by e-mail (check the top right) you don’t have to remember to check for updates, the updates will come to you. =) It’s up to you of course, just wanted to make sure you knew about those options.
The question of whether mathematicians are more creators or discoverers is an interesting one, and gets to the heart of some of the debates on the philosophy of mathematics. Personally, I agree with you that mathematicians are discoverers more than creators, but there’s still a lot of art involved in the exploration and presentation of math. (Most) mathematicians do mathematics because it is exciting and beautiful, not to win fame and glory for discovering something. The highest compliment a mathematician can give to another’s work is not that it is “extremely correct” but that it is extremely elegant or beautiful.
I was wondering… glad to see you back.
I don’t care for the Lockhart piece. Broad generalizations, a very iffy analogy, and then? A few small examples with none of the scope his lofty prose promises. He’s not the first to dislike traditional proofs in geometry. But he wants to redo K-12 based on that? The positive examples he give don’t need curricula to be reworked.
Also, note the date. This was written during the height of the math wars, where lots of people were arguing hard about what should or should not be taught. But this piece does not touch any of that. Unaware? Thought the issues were unimportant? I don’t know. But in that context, the “Lament” does seem to be at least a bit self-indulgent.
Hey Brent,
I am very happy for you, if belatedly. I can direct you to good gelato and Ethiopian food in Philadelphia, since I lived there a year ago. Please enjoy, I am seriously excited for you, and for me as I hear about your grad student life! Seriously.
Hi Jonathan,
Thanks! Good gelato and Ethiopian sound great, we definitely appreciate tips from current or former locals on things to see, do and eat. Anyway, I’m glad you will vicariously enjoy my grad student experience, I’ll be sure to keep you updated! =)
I read Lockhart’s Lament today.
I love that passage. Really a lot of the essay made me break into a grin because it recalled to me the minds and enthusiasm of some friends I was fortunate to have met at college. If not for them and my brushes with their great teachers I never would have had an idea of what Math could be, why it was more than tricks.
I don’t agree with the guy with blue version of my name above. The analogy to music feels strong enough to me, though I do think using the artist’s dream is unnecessary and in fact a come-down from the music example. Which is a microcosm of what is really wrong with the piece: it is long, largely due to his trying making the case in many different ways the case that math is a perverted awful shell of what it could be. He attacks bad textbook writing, quibbling with notation, misguided personification and much more—he’s already cut off the head of the beast and then wants to hack at the limbs. It’s an odd paradox that probably only members of the choir would have the motivation to read the whole thing . . . I think it shows that he wrote it first for himself, and probably did not team up with a friendly layman editor.
I don’t by any means agree with everything he’s said and of course doubt the practicality, as I must. I wonder how many math professors, who depend upon their students having a rather extensive foundation in basics, would actually endorse the destruction of today’s rigorously tiered math curriculum. But it was an instructive piece for me, and good enough for me to deem worth sending to my math teacher friend.
Jonathan: I hope your math teacher friend was as offended as I was about Lockhart’s characterization of the field of Education (ie. teacher’s colleges, methodology, pedagogy, etc) as a “crock” while romanticizing his field of choice as “art.” Offensive and inaccurate.
We all see art in the fields that we have chosen, but like ACTUAL art, the beauty is in the eye of the beholder. Perhaps the reason that so many people dislike math isn’t because incompetent teachers are teaching an unsatisfactory math curriculum, but because that particular art is jarring and unpleasant to them.
In singing the praises of his art, Lockhart denounces mine, and that’s simply offensive. As the other Jonathan states, this piece is quite self-indulgent and demonstrates a real lack of understanding about how the school system and teaching actually works.
Gerry: The beauty of a piece of art, as you say, is in the eye of the beholder, but you are completely in denial to think that the reason kids hate math is because of a valid, information based opinion. Kids hate math because they DON’T get it: it’s associated with a stuffy classroom, an old fart of a teacher, and ridiculous traditions and rules with utterly no significance. Maybe if the majority of kids were supplied with a competent, inspiring teacher, then they would understand the beauty that is math. It is no less beautiful, it is just less accessible because it is that much more abstract. Also, Paul isn’t insulting teachers, but the educational setup we have nowadays: where uninspired people go into classrooms and in the most regimented, tedious way, force information down the throats of uninterested students. Don’t you see a problem there? Again, something that can’t be denied.