Known Unknowns

Popular books about physics and math can be a recipe for frustration. There's a lot of basic ground that needs to be covered to explain any given modern topic—like what Newton did and why Aristotle was wrong, or how the Greeks invented geometry and the Indians the number zero. Not only is the same ground paced over, but the metaphors used to detail that ground are often identical. It's a hard thing to write a popularization of math that is original, and even harder to write one that is both correct to someone who knows about the subject, and understandable to someone who doesn't (which is the intended audience, after all). Sacrifices are necessary; as John Derbyshire writes in Unknown Quantity, his history of algebra published in 2006, "I hope only to show what algebraic ideas are like."

He succeeds in doing so, both in this book and in another, earlier book, Prime Obsession, an accounting of the Riemann hypothesis, which similarly conveys what analytic number theory is like.