Five Golden Rules: Great Theories of 20th-Century Mathematics--and Why They Matter

What do mathematicians do all day, and why in the world should we care? Science writer John L. Casti approaches these questions with characteristic flair in Five Golden Rules, a short work explaining five important 20th-century mathematical theories and their importance in our daily lives. The reader is left with a new appreciation for the men and women who are paid to do little but think and convince their peers that their thoughts are important. Von Neumann's minimax theorem, crucial for modern economics and military strategy, is first up, and Casti expresses its simple elegance in terms that even those with the rustiest high school math can handle. Four other theories, covering topology, computing, optimization, and singularities, get their turn, and each is a work of beauty much like the greatest poems or paintings of our time. Some of the practical applications are surprising (who knew that geometrical analysis can tell us if a joke will be funny?) but more surprising still is our general ignorance of the role math plays in our lives. Though the material gets more involved as the book progresses, elementary algebra and geometry, coupled with a willingness to work things out before proceeding, will suffice for most readers. Casti has once again gifted us with a clear, penetrating book covering a subject still largely uncovered. Five Golden Rules will make math real even to the most hardened number-phobe. --Rob Lightner