Arithmetic has always been a problem for me. I understood the practical reasons for addition, subtraction, multiplication and division, and got through them despite the dull repetition of it, but when I reached the age for algebra and geometry, I was totally bewildered. No one explained to my satisfaction why I should know any of those abstruse formulas and odd lot symbols. Engineers and architects, maybe. But me, the perpetual English and philosophy student?
When I got to college, I found out about logic, which in those days was a very important part of the study of philosophy. So central in most college programs that I left the field. Nonetheless, even though I wasn’t much good at it, I came to like it and to understand, from that perspective, that mathematics was much more important than I’d thought. I have a vague memory of listening in a San Francisco living room to a mathematician to whom higher mathematics contained the secret of the holy grail. I came to understand that it was a way of describing the universe—the universe as it was understood centuries ago, and today. For many who worked in mathematics, it was a spiritual thing. If I’d known that when I was a kid, who knows what I might have learned—or at least wanted to learn?
I also began to understand that music is mathematical, and how could I not love it then, even if from a great distance?
The other day, I ran into the oddest article in Prospect Magazine, a United Kingdom publication. Entitled, “Playing with infinity on Rikers Island,” it’s about the author’s relationship to mathematics. “I had strong anti-mathematical and sentimental leanings as a child,” writes David McConnell. “Maths seemed to reduce pretty things like the moon and roses to ugly things like orbital periods and Mendelian tables.” I was only later that he had the revelation that mathematics was “pure thought.”
As an adult he found himself teaching prisoners and school dropouts who were working for their GEDs. When one of his students admired him as he struggled with a clumsy mathematical problem, because, unlike other teachers she’d known, he didn’t pretend “to know everything,” he writes:
I said it wasn’t the knowledge itself that was valuable—although she was going to have to master enough for her GED—it was, as my history teacher used to insist, the habit of thinking clearly.
I demonstrated this by showing her a habit I had when adding columns of numbers on a piece of scratch paper. Pen in hand, I wrote the digits in a column and made a bold line underneath,. I ‘added’ this way: I tapped the point of my pen on the paper the number of times represented by the digit I wanted to add. With ‘3’ I tapped the three points of the written Arabic numeral. With 4’ and ‘5’ I tapped four or five imaginary sections of each numeral. With numbers like “7” I tapped a little figure of dots off to the side.
As she watched my monkey-like literalness, my student appeared to doubt me as a math teacher. I argued that this was a primitive but pretty way of thinking mathematically. With my taps I was drawing the numerals out in time and space. I was translating the numeric abstractions of the column of Arabic numerals into an intuitive, music-like beating of time, a 1 + 1 + 1 + 1 + 1 + 1…..
And besides this music of time, I’d also produced the tiny geometric figures my tapped points formed. Simplistic as it appeared, here was the multidimensionality characteristic of mathematical understanding. My student, who was much more talented than I, was soon capable of finding other, beautiful mathematical relationships—some I hadn’t even noticed myself.”
Ah, if only I had had a teacher like that. Maths would have added whole new dimensions to my life!