Before paul hoffman came along, Paul Erds was famous only among mathematicians. Erds (pronounced air-dish) was an impish, amphetamine-swallowing number theorist from Hungary who lived out of a shabby suitcase, gave nearly every waking moment to mathematics and published more than 1,400 papers, making him one of the most prolific mathematicians of all time. Colleagues in dozens of countries adopted him as their itinerant “Uncle Paul” and saved up their thorniest math problems for his visits. But after Hoffman profiled him in The Atlantic, Erds’ renown grew logarithmically, so much so that The New York Times felt obliged to run a 1,200-word obituary on his death in 1996.

Erds was the kind of subject magazine writers kill for: brilliant and eccentric, with a colorful history and a penchant for advertising his irreverent philosophy of life. But to evoke in readers the same mixture of amusement and awe Erds’ colleagues felt toward him, while simultaneously explaining Erds’ lifelong love for numbers, required a writer with Hoffman’s special literary and intellectual skills.

(Ironically, Hoffman’s book isn’t the only one on Erds coming out now. A second book, by Bruce Schechter, My Brain Is Open, published by Simon & Schuster, includes many of the same stories but covers more number theory. Schechter, a science writer with a PhD in physics, writes less alluringly than Hoffman but provides extra background for readers who may crave more mathematical meat.)

Hoffman’s book, based on the Atlantic article, is structured around anecdotes from Erds’ peculiar life, but it is less a biography than a highly successful popularization of number theory and its history. Comical passages describing Erds’ eccentricities such as his amnesia for everything nonmathematical (every time he was served rice he had to ask what it was) are plentiful, but they serve primarily as interludes.

In the book’s main passages, Hoffman takes forbidding mathematical issues related to Erds’ work and explains them with lucidity and infectious pleasure. Having read this I think I comprehend for the first time why it’s always better to switch doors in the Monty Hall dilemma, and why the counting numbers increase to infinity but the supply of real numbers and transcendental numbers such as e and is infinitely larger than this infinity. If “mathematics is the only infinite human activity,” as Erds liked to say to explain his own interest in numbers, then it’s lucky we have people like Hoffman to make it a little more finite for the rest of us.