Hawking, God & The Math Ed Train Wreck
Stephen Hawking, the most famous physicist since Einstein, recently denounced heaven as "a fairy story for people afraid of the dark." This is another of Hawking's shots fired in the (alleged) war between science and religion. Hawking's prediction, of course, is that "Science will win." His recent book, The Grand Design, is his contribution to coming victory, and in it, he argues that God did not create the universe.
Hawking bases his claim on an interpretation of a new scientific theory, called M-theory (everyone's a bit unclear about what the 'M' stands for). M-theory's mathematics, says Hawking, tells us the universe was created by quantum fluctuations out of nothing, and that ours is merely one of very, very many existing universes.
Now, perhaps Hawking is right. Then again, perhaps not. But to determine which, we'll need to know some physics -- quite a bit of it. After all, M-theory is a physical theory. Moreover, to grasp physics we'll need a healthy dose of mathematics, since most of contemporary physics is expressible only in the language of mathematics.
Unfortunately, most of us are just pathetic at math, harboring a fear and hatred of it to boot. And so there is weeping and gnashing of teeth throughout academia. The problem, everyone acknowledges, is that math education is a train wreck.
The real question is, "Why is it such a wreck?"
The answer is simplicity itself. There are two main problems. One is that we only teach students how to do math. The other problem is that we try to teach them too much mathematics.
Regarding the first problem, we've failed -- and failed miserably -- to show students how mathematics has always been central to our intellectual culture. And who could blame us: we weren't told. The solution here -- and we have a long way to go -- is to teach students the integrated history of math, science, and philosophy. In fact, because these disciplines grew up together, we won't understand any of them properly without understanding this shared history. We have here a three-legged stool that's really wobbly without all of its legs.
The goal of telling the integrated history isn't to get kids excited about math. Neither is it to help them understand mathematical concepts so they can do math better. (Although in my experience, it has certainly done these things.) The ultimate significance of telling this story -- and the point of education in general -- is to teach students how to be better humans. And it is surprising how much the story of mathematics teaches us about ourselves.
But the second problem (that of covering too many mathematical topics) is much more dire. I'm dumbfounded at how many times the student's understanding of mathematics takes a back seat to reaching the end of a textbook, or to covering a certain list of topics before the student graduates. When a schedule becomes a tyrant, math courses go altogether too quickly, moving past topics before any of them take real root. This results in tissue-thin mathematical knowledge. Breadth is a fine thing, but breadth suffers from shallowness. Thin veneers quickly rub off.
Ironically, by covering less material better, average high school students can easily learn calculus before they graduate. The path to calculus is much shorter than you might think, as long as that path is direct. But we'll need to ignore all the distracting adulterations. I've had students whose faces blanch at the mere mention of math, students who know only a smidge of algebra, and in eight weeks, I've taught them the fundamentals of calculus (I do this by sticking to polynomials). Many of these students are delighted to discover that they don't have a genetic math disorder. Once they understand the point of calculus, they can then move on to its more complex applications. And this is much more effective if the foundation is well laid, and given some time to cure.
So then, physicists like Hawking will continue to make substantial claims about God based on science. Many of these claims lack decent support, at best. But we won't really know this unless we know our math.
Mathematics is, in a sense, a religious discipline.
But, then, most disciplines are.