A few years ago, I decided to study mathematics because I thought it would make me smarter. I also hoped to correct a flaw in my past, since I had failed mathematics decisively and serially and only got through it by cheating. I had done fine with arithmetic, but I entered the woods when words became equations and x’s and y’s. I had a block of some kind. Some people are tone deaf; I appeared to be math deaf.
I decided to begin where I had got thrown off the math train, at Algebra Junction. After that I planned to learn geometry and calculus, the three parts of what the 18th century called “pure mathematics.” Algebra was harder than I thought it would be. I assumed I had grown smarter since childhood, and I expected to coast through algebra wondering why I had found it so challenging. I still felt resentful at how math had treated me, though, and this led to my having a poor attitude. Moreover, I was pretty sure math was wrong, and I meant to prove it.
While I struggled with how long the train from Omaha would take to reach Denver if the trip were 500 miles and the train were traveling 43 miles an hour for the first half of the trip and 62 miles an hour for the second half and the trip took eight hours and so on, I was also reading about mathematics. To my everlasting surprise, I learned that math, which had seemed the exemplification of practicality, is also as mysterious as any scripture, as well as being older than any scripture. I might say it is a scripture itself, at least of a kind, except an infallible one.
As it turned out, I couldn’t do mathematics much better as an adult than I had been able to as a child, but I could think about mathematics, because anyone can, and thinking came to be what interested me. Mathematics has a huge, perhaps near infinite catalogue of mysteries, only a few of which I am acquainted with or understand, but the simplest one, the starter one, waiting like a welcoming party in the vestibule of mathematics, concerns the origin of numbers.
No one knows where numbers come from. No culture has a story where a creature or a spirit gives numbers to humans. No one in any text I ever found climbs a mountain and gets numbers or finds numbers while wandering in the desert. So far as I know, no country has a holiday for the day they got numbers, either. Numbers seem simply always to have been here, exemplifying Plato’s belief in a non-spatiotemporal realm, the timeless nowhere which has never existed anywhere and never will but which nevertheless is.
To my everlasting surprise, I learned that math, which had seemed the exemplification of practicality, is also as mysterious as any scripture, as well as being older than any scripture.
From the perfect objects in the non-spatiotemporal world the imperfect objects of our own world are made. Man gave names to numbers, but the names are merely descriptive. The qualities they denote are inherent in collections and were present before anyone described them. Numbers in this sense are like a river which exists before anyone gives it a name.
The formulas and equations and mathematical remarks that mostly rebuffed me are themselves the façade of an infinitely capacious structure of thought and speculation. A simple question is: Who built the façade? Which is another way of asking, Is mathematics discovered or created?
If, like most mathematicians, I think that mathematics is discovered, then it has a perfection, an orderliness, and a permanence that a human mind cannot achieve on its own. If I think that mathematics is a system created by human beings, then it is necessarily imperfect, opportunistically ordered, and parts of it are impermanent since it reflects human misconceptions and shortcomings, which require revision, and perfection is an abstraction anyway.
But if discovered, discovered where? And how does it come to be there? Was a divine force involved? I don’t know, of course, and no one else does, either. Mathematics is one of the places where we come close to the great secret.
Alec Wilkinson is a journalist and the author of several books. His latest, A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age, will be published by Farrar, Straus and Giroux on July 12
