This book leaves me breathless!

A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form by Paul Lockhart


As regular readers of this blog perhaps remember, my intellectual journey began with a love of mathematics. Through high school I kept a "mathematics journal", which I still have in several volumes, posing and trying to solve problems, largely in number theory. I was good enough in math and science to be one of the 100 Freshmen admitted to Cal Tech in 1957. And there I had a great reality check.


Even though I was "good enough" to publish a number theory article in a math journal my sophomore year, I knew I wasn't "good enough" to reach my dreams as a mathematician. I knew because I met a few contemporaries who were good enough. I realized, for the first time in my life, I had limited options in mathematics. It's like being an undefeated high school miler who goes to college and suddenly finds himself easily beaten by several other runners. My response was confusion, frustration, bewilderment -- and leaving Cal Tech, even though I had a B average. Breaking my mother's heart in the process. Less than a year later I was in the Army, the best place for me at the time (given the draft).


I say this to remind you that I know a little about math. So when Paul Lockhart, in this remarkable slim book that crucifies the way we teach math in our schools, says that mathematics is an art form, I say, Right on! It's about time somebody spoke this basic truth. 


I've said here before that I see very little difference between the self that scribbled in his math journal in high school and the later self who scribbled plays and novels and poems. In each case I was striving for order, for structure, for economy, for eternity. In high school I wanted to say something true and eternal about the nature of numbers. Later, as a writer, I wanted to say something true and eternal about the nature of humans. In each case, my personal aesthetic of "less is more" worked to say this as efficiently, cleanly, elegantly as possible.


A mathematician = a playwright = a novelist = a poet. The tools, the language, change but the work, the activity, the quest, have far more in common than different.


And this is Lockhart's argument. Clearly no one reading this, who hasn't learned about mathematics on their own, quite believes it because this is not the "math experience" in our schools. Not even close. And this infuriates Lockhart. And it infuriates me.


Listen to some of the remarkable and true things he has to say.

THE FIRST THING TO UNDERSTAND IS THAT MATHEMATICS is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such. Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound. In fact, our society is rather generous when it comes to creative expression; architects, chefs, and even television directors are considered to be working artists. So why not mathematicians? Part of the problem is that nobody has the faintest idea what it is that mathematicians do.

 A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

 If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. 

 You don’t need to make math interesting—it’s already more interesting than we can handle! And the glory of it is its complete irrelevance to our lives. That’s why it’s so fun!

 English teachers know that spelling and pronunciation are best learned in a context of reading and writing. History teachers know that names and dates are uninteresting when removed from the unfolding backstory of events. Why does mathematics education remain stuck in the nineteenth century?

 There is such breathtaking depth and heartbreaking beauty in this ancient art form. How ironic that people dismiss mathematics as the antithesis of creativity. They are missing out on an art form older than any book, more profound than any poem, and more abstract than any abstract. And it is school that has done this! What a sad endless cycle of innocent teachers inflicting damage upon innocent students. We could all be having so much more fun.

This book began as an essay passed secretly from math teacher to math teacher, like some banned Russian novel, until a math columnist found it and tracked down the writer, telling him how important this message was and that it deserved expansion into a book. Here it is, published a few years ago. I doubt if it will make any difference. But how incredibly beneficial if it could make a difference!

I'm not sure I could understand my high school math journals today but this book makes want to peek inside and find out.