Letters to a Young Mathematician Read Free Page B

done a year’s more math and had been practicing for weeks; we had five minutes’ warning. I came in first, and my friends were second and third.
    So the headmaster had no choice but to let us take the exam for the State Scholarship. After all, he was letting the older kids take it, and we had proved we were better prepared for it than they were.
    All three of us were awarded State Scholarships.
    At that point Mr. Radford got in touch with David Epstein, whom he had taught some years before and who had become a mathematician at Cambridge University, along with Oxford, the United Kingdom’s leading university, especially renowned for its math.
    “What do I do with this boy?” Gordon asked.
    “Send him to us,” said David.
    So I went to study math at Cambridge, the home of Isaac Newton, Bertrand Russell, and Ludwig Wittgenstein (along with many lesser lights), and I never looked back.
    Some careers seem to accumulate people who might easily have preferred to do something else. You will run into people who tell you that they practice law as a day job but they are really novelists or playwrights or jazz trombonists. Other people can’t settle on something, or they see their careers in more purely practical terms, and they drift into human resources management or advertising sales. Which is not to say that these people are not dedicated or fulfilled in what they do, but few of them consider their work a calling .
    No one drifts into being a mathematician. On the contrary, it’s a pursuit from which even the talented are too easily turned away. If I hadn’t broken my collarbone, if Mr. Beck hadn’t fostered all-out competition among his students, if there hadn’t been an unusually large group of strong students for Mr. Radford to promote— and if he hadn’t done it so aggressively—instead of writing you today I might be telling your parents how to save more on their tax return. And perhaps no one, least of all me, would suspect that things could have turned out differently.
    In short, Meg, you should not expect your teachers to look at you once and simply see, in a brief glance, how bright you are. You should not expect them to unerringlyspot your talents and know where they might lead you.
Some will, and you will be grateful to them for the rest of your life. But others, sadly, can’t tell, or don’t much care, or are caught up in their own worries and resentments. Then again, the ones who stand in awe of your gifts are not the ones from whom you will ultimately learn the most. The best teachers will occasionally, perhaps more than occasionally, make you feel a bit stupid.

3
The Breadth of Mathematics
    Dear Meg,
    It’s not hard to see, in your question, a sense of—I don’t know—anticipated boredom, or perhaps some worry about what you’ve let yourself in for. It’s all reasonably interesting now, but, as you say, “Is this all there is?” You’re reading Shakespeare, Dickens, and T. S. Eliot in your English class, and you can reasonably assume that while this is of course only a tiny sample of the world’s great writing, there is not some higher level of English literature whose existence has not been disclosed to you. So you naturally wonder, by analogy, whether the math you’re learning in high school is what mathematics is. Does anything happen at higher levels besides bigger numbers and harder calculations?
    What you’ve seen so far is not really the main event.
    Mathematicians do not spend most of their time doing numerical calculations, even though calculations are sometimes essential to making progress. They do notoccupy themselves with grinding out symbolic formulas, but formulas can nonetheless be indispensable. The school math you are learning is mainly some basic tricks of the trade, and how to use them in very simple contexts. If we were talking woodwork, it’s like learning to use a hammer to drive a nail, or a saw to cut wood to size. You never see a lathe or an electric drill, you do