Letters to a Young Mathematician Read Free

also look at animals differently, because I’m aware of the mathematical patterns that underlie their movements. When I look at a crystal, I am aware of the beauties of its atomic lattice as well as the charm of its colors. I see mathematics in waves and sand dunes, in the rising and the setting of the sun, in raindrops splashing in a puddle, even in birds sitting on telephone cables. And I’m aware—dimly, as if looking out over a foggy ocean—of the infinity of things we don’t know about these everyday wonders.
    Then there’s the inner beauty of mathematics, which should not be underrated. Math done “for its own sake” can be exquisitely beautiful and elegant. Not the “sums” we all do at school; as individuals those are mostly ugly and formless, although the general principles that govern them have their own kind of beauty. It’s the ideas, the generalities, the sudden flashes of insight, the realization that trying to trisect an angle with straightedge and compass is like trying to prove that 3 is an even number, that it makes perfect sense that you can’t construct a regular seven-sided polygon but you can construct one with seventeen sides, that there is no way to untie an overhand knot, and why some infinities are bigger than others whereas some that ought to be bigger are actually equal, that the only square number (other than 1, if you want to be picky) that is the sumof consecutive squares, 1 + 4 + 9 + . . ., is the number 4900.
    You, Meg, have the potential to become an accomplished mathematician. You have a logical mind and also an inquiring one. You’re not convinced by vague arguments; you want to see the details and check them out for yourself. You don’t just want to know how to make things work, you want to know why they work. And your letter made me hope that you’ll come to see mathematics as I see it, as something fascinating and beautiful, a way of seeing the world that is like no other.
    I hope this sets the scene for you.
    Yours, Ian

2
How I Almost Became a Lawyer
    Dear Meg,
    You ask how I got into mathematics. As with anyone, it was a combination of talent (there’s no point in being modest), encouragement, and the right sort of accident, or more accurately, being rescued from the wrong sort of accident.
    I was good at math from the start, but when I was seven, I very nearly got put off the subject for life. There was a math test, and we were supposed to subtract the numbers, but I did the same as the previous week and added them. So I got a zero and was put in the lower section of the class. Because the other kids in that section were hopeless at math, we didn’t do anything interesting. I wasn’t being challenged, and I got bored.
    I was saved by two things: a broken bone and my mom.
    One of the other kids pushed me over in the playground as part of a game, and I broke my collarbone. Iwas out of school for five weeks, so Mom decided to make good use of the time. She borrowed the arithmetic book from the school, and we did some remedial work. Because I couldn’t write—my right hand was in a sling—I dictated the numbers, and she wrote them in the exercise book.
    My mother was rather sensitive about schooling. Her own education had been pretty much ruined by the mistaken good intentions of a well-meaning but unimaginative school inspector. Because she was quick on the uptake, she was advanced rapidly through the grades until, by the age of eight, she was in with a class of ten-year-olds. The school inspector came by one day, observed the class, and asked the intelligent little girl who was answering all the questions, “How old are you, my dear?” On being told “eight,” he informed the school principal that the bright little girl must stay in the same class for three years in a row, until the other kids her age caught up with her. He wasn’t trying to hold her back academically; he was worried that she was out of her depth socially. But repeating the same lessons three