But I have now come to know many people I consider intelligent and thoughtful who never got anything out of math. They never saw any beauty or power in it, never experienced it as anything but suffering. So as part of my long-term struggle to resist imposing my personal views on others I have stopped evangelizing for more math and begun thinking about what we might teach instead of algebra.
But then there's this from Alec Wilkinson, who hated math as a kid but went back to restudy it at the age of 60 (NY Times):
Mathematics, I now see, is important because it expands the world. It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person play close attention. To be made to consider a problem carefully discourages scattershot and slovenly thinking and encourages systematic thought, an advantage, so far as I can tell, in all endeavors. Abraham Lincoln said he spent a year reading Euclid in order to learn to think logically.
Studying adolescent mathematics, a person is crossing territory on which footprints have been left since antiquity. Some of the trails have been made by distinguished figures, but the bulk of them have been left by ordinary people like me. As a boy, trying to follow a path in a failing light, I never saw the mysteries I was moving among, but on my second pass I began to. Nothing had changed about math, but I had changed. The person I had become was someone whom I couldn’t have imagined as an adolescent. Math was different, because I was different.
The beginner math mystery, available to anyone, concerns the origin of numbers. It’s a simple speculation: Where do numbers come from? No one knows. Were they invented by human beings? Hard to say. They appear to be embedded in the world in ways that we can’t completely comprehend. They began as measurements of quantities and grew into the means for the most precise expressions of the physical world — e = mc², for example.
The second mystery is that of prime numbers, those numbers such as 2, 3, 5, 7, 11 and 13 that can be divided cleanly only by one or by themselves. All numbers not prime are called composite numbers, and all composite numbers are the result of a unique arrangement of primes: 2 x 2 = 4. 2 x 3= 6. 2 x 2 x 2 = 8. 3 x 3= 9. 2 x 3 x 3 x 37 = 666. 29 x 31 = 899. 2 x 2 x 2 x 5 x 5 x 5 = 1,000. If human beings invented numbers and counting, then how is it that there are numbers such as primes that have attributes no one gave them? The grand and enfolding mystery is whether mathematics is created by human beings or exists independently of us in a territory adjacent to the actual world, the location of which no one can specify. Plato called it the non-spatiotemporal realm. It is the timeless nowhere that never has and never will exist anywhere but that nevertheless is.
Mathematics is one of the most efficient means of approaching the great secret, of considering what lies past all that we can see or presently imagine. Mathematics doesn’t describe the secret so much as it implies that there is one.
The young Lincoln's fascination with geometry is worth pausing over. Many European intellectuals shared it, because for 2200 years Euclid's geometry was how young pupils were introduced to logical proof. There are hundreds of anecdotes about young intellectuals who were captivated by this magic. I was one. So I was rather shocked to discover that the state of Maryland no longer teaches Euclid, and you can now complete geometry class without proving anything. Instead of learning how to derive the formulae from simple principles you just have to memorize them.
Anyway there is this to be said about math education: as it is it may mainly spread suffering, but if we did not force it on people then many thousands who are susceptible to this magic would never get the chance to experience it.