DRIVEN TO ABSTRACTION: Devlin with Mark di Suvero’s sculptural homage to a mathematician, The Sieve of Eratosthenes, installed on campus in 2000. Rod Searcey

radio fans who listen to National Public Radio’s “Math Guy” might be surprised to learn that the Stanford mathematician has yet to teach a course on campus. After all, Keith Devlin has built an unlikely following on a difficult subject with his breezy insight. He’s “a great teacher and a superb communicator—he has a way of making you excited to see the strings of math that pull on our lives,” says Weekend Edition’s host, Scott Simon. “We have the math slot only because it’s Keith.”

At Stanford, Devlin has been fully occupied since 2001 as executive director of the Center for the Study of Language and Information, where he applies mathematics to human-computer interactions and helped start the multidisciplinary Media X program. But he applies his teaching skills in other ways. Devlin contributes a lively monthly column to the Mathematical Association of America website—one recent topic was the demonstrably nonrandom quality of “random” airport security checks. He has also written a string of math books for general readers.

William Frucht, his editor at Basic Books, says most authors are either entertaining or accurate on the subject, not both. “Keith is one of the few people who manage to write entertainingly about math and yet can be trusted. He’s the only person I know who could not only explain group theory but actually make it sound simple.”

That’s what convinced Frucht, despite Devlin’s protests, that the author was up to the challenge of describing what the mathematical community considers the seven greatest unsolved math problems of our time. The result: his latest book, The Millennium Problems (Basic Books, 2002).

In it, Devlin explains why modern math is so hard for non-mathematicians to grasp. Whereas it’s possible to explain the gist of state-of-the-art physics and biology research in a few paragraphs, today’s math is too abstract for a general audience. With this caveat, Devlin proceeds to lead readers up the chain of abstractions necessary to appreciate the nature, history and significance of each problem—even the inscrutable Hodge Conjecture, which Devlin says he himself doesn’t fully understand. His goal: to make the book accessible to anyone with a good high-school math education and a strong interest in the subject.

Devlin, a native of England, has been writing about math for a general audience for 20 years, ever since, just for fun, he submitted an April Fool’s story to the Guardian, a British daily. The idea was to report a true mathematical result so improbable that readers would take it as a hoax. The paper’s science editor, Tim Radford, says Devlin’s work was so “gleaming and enjoyable” that he made him a columnist, a gig that lasted until 1989. His collected columns were published as All the Math That’s Fit to Print (Mathematical Association of America, 1994). By then, Devlin had moved to the United States, becoming dean of science at St. Mary’s College in Moraga, Calif., before joining Stanford.

Born into a working-class family in a rough dockside area of Hull, young Devlin seemed an unlikely candidate for college, let alone graduate school in mathematics. But he passed the exam that in brutally efficient, binary fashion permanently placed all 11-year-olds in postwar England on either the college-prep or vocational track.

‘Calculus is just magical. It gives you answers to problems that by all rights you shouldn’t have answers to.’

Devlin says he hated math in elementary school and passed the 11-plus mainly on the strength of his verbal skills. But the Soviets’ launch of the Sputnik satellite in 1957 so excited him that, like many of his generation, he set his mind on becoming a scientist. “I was remarkably ignorant of what science was about,” he says in his rolling Yorkshire accent, “but pioneering was clearly the appeal.”

To do well in science, Devlin dutifully applied himself to his math studies—which he found unexciting until he got to calculus. “Calculus is just magical,” he says. “It gives you answers to problems that by all rights you shouldn’t have answers to.” For the first time, he saw mathematics as a subject full of beauty and wonder all its own.

After earning his PhD, he started sharing his passion, first in obscure research monographs, then in graduate and undergraduate textbooks. He worked to enhance his prose style by analyzing writers he admired, especially Martin Gardner, the legendary math popularizer.

“It’s all about getting the right metaphors,” says Devlin. In a calculus CD-ROM, Devlin introduces the principle behind integration by slicing an onion. “The more abstract the concept that you want to explain, the more concrete and earthy the metaphor must be,” he says.

Devlin uses the London Underground map to show what topology is all about in The Millennium Problems. First, he notes that while the map’s scale, distances, straightness and geographical directions of the subway lines don’t conform to reality, the depiction of the network (i.e. the order of the stations and the places where lines intersect) is correct. As Devlin explains,

If the Underground map were printed on a perfectly elastic sheet of rubber, it could be stretched and compressed so that every detail was correct, giving a standard, geographically accurate map, drawn to scale, with every stretch of line correctly oriented to the compass bearings. This stretching would not affect the way the lines connect the various stations. The reason, in mathematical terms, is that networks are topological objects. You can twist or stretch any of the connecting lines in a network without changing the overall configuration. To change the network, you must either break a connection or add a new one.

He points out that the same holds true for electrical circuits, computer chips and the Internet. “This is why ‘rubber-sheet geometry’ is one of the most important branches of mathematics in the world today,” Devlin writes.

Devlin also knows how to tell a story. A chapter in The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip (Basic Books, 2000) begins with an ingenious allegory of “Emily X,” a disturbed mathematical prodigy who mysteriously disappears for several years only to return with cryptic accounts of her lost time. Storytelling is indispensable in The Millennium Problems, which would leave many readers out in the cold without its accounts of the generations of mathematicians whose work led to each problem.

Articulate and personable, Devlin belies the stereotype of the reclusive, socially inept mathematician. But he concedes there’s some truth to the image. Mathematicians’ work, he says, is judged solely on the quality of the results, and personality will get you nowhere. Also, as he explains in The Math Gene, the best mathematicians are people to whom the abstract feels intensely real, occasionally making them act absentminded when the real world intrudes.

Still, the central thesis of The Math Gene is that we all have the capacity for mathematical thinking, just as we do for language. Those who doubt might try tuning in to the Math Guy.

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