In 2000 the Clay Mathematics Institute offered a cool million bucks for the answer to any of the seven math problems that they've deemed the hardest in the world. The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time is an attempt by Keith Devlin (NPR's "Math Guy") to describe those seven problems in layperson's terms. Don't get your hopes up, though; after reading it you still will have no shot at the million--the problems are very, very hard--but you will at the very least have a new appreciation for those who do.
Devlin wastes no time. His brief introduction describes the problems and their importance to the field of mathematics, and then he dives right in. The next seven chapters break down each of the seven problems. Formulas fly, and the problems become increasingly more difficult to understand. The difficulty of the final problem is so great, Devlin is forced to give a disclaimer: "The Hodge Conjecture... is easily the least accessible of the Millennium problems," he writes. "It deals with objects that are so far removed from the intuitions of even the experts that not only is there no 'smart money' on whether the conjecture will turn out to be true or false, there isn't even a consensus as to what it really says." Ouch.
At times Devlin seems more intimidated by the problems than his readers will be. "I knew from the start that no matter how hard I tried, I could not make this book an easy read," he writes in the preface.
Certainly the book is no dimestore paperback, but Devlin maintains an energetic and entertaining pace throughout. He has an impressive gift for simplifying technical jargon and offsets the baffling equations and numbers behind each problem by showing their relevance to the fields of science and industry--their solutions could affect industry, airplane safety, and even Internet security.
Also interesting are Devlin's historical accounts of the brilliant people that created the problems. Indeed, the book's ultimate success is in shining a bright light on the mysteries of the human mind and the truly dizzying heights it can achieve. AARON BEAM