The Sciences

Keith Devlin—The Joy of Math


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Keith Devlin has strange news for those who believe that math is medieval torture: deep down, he says, we're all mathematicians. Devlin, a mathematician and dean of science at St. Mary's College in Moraga, California, explains why in his latest book, "The Math Gene: How Mathematical Thinking Evolved and Why Numbers are Like Gossip." (Basic Books, 2000). Apparently math is ingrained in our brains, an offshoot of our unique grasp of language. He shared his numerical musings with Discover associate editor Josie Glausiusz.

How did math arise from language? The structural change in the brain that gave us language was precisely the change that gave us mathematical ability. Math— the ability to create abstractions and symbolic representations of things, which is what words are— came as a freebie. In fact, math IS a language in several ways. The language of mathematics as a written thing is a mixture of words and symbols, and there are restrictions on how to use those, just as there are for ordinary language.

When did humans first use math in a conscious way? Our ancestors acquired vocabulary and a proto-language over a couple of million years, and then between 75,000 and 200,000 years ago the brain acquired the ability to create sentences. Around 8000 B.C., the Sumerians hit upon the trick of inventing these things called numbers. It was the Greeks in 600 B.C. who began consciously to think about it. Indeed, the Greeks were so enamored by the study of numbers and geometry and mathematics that they put it at the center of their civilization.

Can you give examples of our intuitive mathematical ability? One is just negotiating our way around in a spatial sense. We're quite good at judging distances and speed when we're driving or crossing streets. I'm not claiming that we explicitly do mathematical calculations in our heads. But the brain has evolved over millions of years to do this automatically and almost effortlessly. And anyone who keeps baseball or bowling scores, or has to use numbers at work, within a very short space of time they get very, very good at it.

Why do so many people hate math? Human beings evolved, first of all, to deal with the physical world and other creatures in it. More recently, our ancestors developed the ability to deal with interpersonal relationships and social structure. But the thing about mathematics is that the objects in it— numbers, triangles— are complete abstractions. Once your brain figures out how to create those abstractions and hold them in the mind whilst you think about them, mathematics actually gets easier by a huge leap.

Can animals do math? Animals and fish that migrate over thousands of miles of land and sea, navigating by the stars and the earth's magnetic field, are clearly doing what we would call trigonometry and geometry. Now, they're not explicitly doing it— using the kind of reasoning where you have symbols written on clay tablets, or drawn on sand or on paper or parchment, with rules for manipulating the symbols. The only good evidence of such [explicit thinking] has been with chimpanzees and bonobo apes. But it takes years of intense training to get them to the stage of a small baby human aged about two. And children don't need that amount of training— they learn instinctively and without any real effort.

Why do you love math so much? I went to high school the year after Sputnik went up [in 1957] and like many people at that time, I wanted to become a scientist. But by the time I was 15 or 16 I suddenly realized that mathematics was much more interesting than the science I thought I was going to use it for. It fell into place as this wonderful, elegant, beautiful, exciting, passionate, emotion-filled world that all hung together. It was like finding a Shangri-La.

Why is math like a soap opera? Mathematicians deal with a collection of objects— numbers, triangles, groups, rings, fields. And what a mathematician does with these objects is ask questions like: "What is the relationship between Objects X and Y? What can X do to Y? If X does this to Y, what will Y do back to X?" It's characters, it's got plot, it's got relationships between them, and it's got life and emotion and passion and love and hate, a bit of everything that you can find in a soap opera. On the other hand, a soap opera isn't going to get you to the moon and back. Mathematics can.

If you could go back into the past and meet any mathematician of your choice, who would it be, and what would you say? I think it would have to be Isaac Newton, because of the huge impact that he had on all of humankind. Now, by all accounts, he was a very quarrelsome, unfriendly, egotistical person. So from everything I've read about him, I wouldn't have enjoyed meeting him. Isaac Newton was not just a mathematician. He was a magician, an alchemist, he was trying to turn lead into gold. Today, most of what Newton did would brand him as a crackpot. However, among all of those things which actually were crackpot things to the modern person was the invention of calculus.

He did it, by the way, when he was only 20 years old. He was a student. What happened was, he went to University at Cambridge, and this was when there was the Great Plague going on, and because of the plague in London and the fears of its spreading up to Cambridge, the University was closed. So suddenly, young Isaac Newton, 20 years old, a beginning student, found himself sent home to his home in Lincolnshire without studies to do. Now, most 20-year-olds would think, "Whoopie! I'll just have a good time for the next semester, the next term." Newton went back home and invented calculus, which is really quite a remarkable achievement.

But I think what I would have said to him if I could meet him, was, "Are you aware of the magnitude of the revolution you've instigated?" and then when he said no, I think I'd try to give him some sense of what people 200 or 300 years later would be doing with the tools that he'd invented. He'd have been blown away by it. No doubt about it.

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