As an erstwhile budding mathematician turned hopeful educator, I try to read a variety of books about math which are directed at the layperson, to get an idea of how writers can successfully pitch math as an interesting subject to a populace that seems determined to see it as esoteric, eggheaded and impossibly obtuse. No book I've ever read has done this as well as The Man who Loved Only Numbers, by Paul Hoffman.
The Man who Loved Only Numbers is ostensibly a biography of a Hungarian man named Paul Erdős, one of the most brilliant and prolific mathematicians of the 20th century: a man who contributed to more mathematics publications than anyone else ever (over fifteen hundred) but never buttered his own toast until the age of twenty-one ("I tried. It wasn't so hard," he said of the experience). In the course of eulogizing the more than sufficiently fascinating Erdős, Hoffman also takes a breathless trip through millenia of mathematical history, philosophy and mythology.
It's important to realize that all the detours into other topics—into international history, into the lives of other famous mathematicians, and into prime number theory and graph theory and worst-case analysis and transfinite numbers—were absolutely necessary to make this book as good as it is. To get an effective portrait of a man whose life was as saturated with mathematics as Erdős's, you have to be prepared to get your hands dirty, to get in and try and understand some of the math that made him tick and drove him to be such a remarkable man, and to get an idea of the breadth and glory of what came before him.
Conversely, there are few better vessels for the appeal of mathematics than Erdős: I don't want to give too many details about all the things that make him a vastly entertaining person to read about, but he was not simply a secluded academic or a socially inept nerd. On the contrary, he was a world traveler, a humble Renaissance man of the mind, a wildly generous philanthropist, and a social butterfly who just happened to have enough eccentricities to make him a goldmine for biographers.
Underneath all that, though, is Erdős's dedication to mathematics.
Near the beginning of The Man who Loved Only Numbers, Paul Hoffman relates a story about his childhood that begins "When I was in grade school, I thought mathematics was about brute computation," and ends with a quote from Erdős: "Mathematics is the surest way to immortality."
Part of what makes this such a remarkable book is that I can see it taking people from where its author was as a kid to the understanding that mathematics is much more than grade school teachers usually let on. Too many people who haven't taken any mathematics past high school suffer from Hoffman's mistaken belief, or some variant of it: that mathematics is just a means to an end, or that it's all about cranking through algorithms and formulas to get "the right answer." I suspect that most people who get out of high school have never seen a real mathematical proof, much less a startlingly elegant one, or even think that such a thing could exist. Most people don't know that pure mathematicians study math not necessarily because it's useful or it will help them land a good job, but because it is, to them, art. It may have a practical use at some point, but that is secondary to its profound aesthetic appeal.
That Hoffman is willing to put on his apron and splash around a bit while painting his portrait of Erdős is not a detriment to this book. He explains several deep and important mathematical results in a way that should be easy to understand even for those who fear math; while this may result in complaints that the book doesn't focus enough on the biographee, it should be understood that the ability to perceive math as a thing of beauty is a prerequisite for trying to understand Paul Erdős. The Man who Loved Only Numbers is written so that anyone, whether or not they have ever seen a mathematical proof, can find some appreciation of Paul Erdős's work, and perhaps more importantly, mathematics in general. That this book might inspire people who think they despise math to take an interest in it makes it something greater than just a biography of Paul Erdős: a celebration of and a tribute to his life's passion.
Hoffman, Paul. The Man who Loved Only Numbers. New York: Hyperion, 1998.
There's another biography of Erdős by Bruce Schechter, entitled My Brain is Open. I haven't read it... yet.