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

FIVE GOLDEN RULES

Great Theories of 20th-Century Mathematics—and Why They Matter

Acclaimed author John L. Casti's fascinating exploration of five monumental mathematical breakthroughs and how they shape our lives

Advance Praise for Five Golden Rules

"With this groundbreaking work, John Casti shows himself to be a great mathematics writer. Five Golden Rules is a feast of rare new delights all made perfectly comprehensible. . .succeeds brilliantly in showing that mathematics applies to the whole spectrum of human thought: physical, metaphysical, and metaphorical." —Rudy Rucker, author of The Fourth Dimension

"Essential reading for anyone who thinks that the abstract results of pure mathematics do not affect their lives. Casti explains the mathematics that is hidden behind many of the everyday things we take for granted. Well written and highly informative." —Keith Devlin, editor of Focus, the newsletter of the Mathematical Association of America, and author of Mathematics: The Science of Patterns

"John Casti has written a wonderful book full of interesting examples that will catch the reader's imagination." —George Dantzig, Stanford University

"This is a first-rate, well-written exposition of several basic ideas in modern mathematics as applied to the world around us, with no compromise on rigor ...science writing at its best." —Martin Shubik, Yale University

With the lucid informality for which he has become known, John Casti has written an engaging and articulate examination of five great mathematical theorems and their myriad applications." —John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper

"Books on mathematics with such beauty, breadth, and insight are rare. Five Golden Rules is replete with intriguing information—not only for curious laypeople but also for seasoned mathematicians and scientists. Casti has produced a truly stunning survey of mathematics' manifold consequences." —Clifford Pickover, IBM T. J. Watson Research Center

"Great theories in mathematics are like great poems, great paintings, or great literature."

from the Preface

In Five Golden Rules, critically acclaimed author John L. Casti serves as curator to a brilliant collection of 20th-century mathematical theories, leading us on a fascinating journey of discovery and insight. Probing the frontiers of modern mathematics, Casti examines the origins of some of the most important findings of this century. This is a tale of mystery and logic, elegance and reason; it is the story of five monumental mathematical breakthroughs and how they shape our lives. All those intrigued by the mathematical process, nonacademics and professionals alike, will find this an enlightening, eye-opening, and entertaining work. High school algebra or geometry—and enthusiasm—are the only prerequisites.

From the theorem that provided the impetus for modern computers to the calculations that sent the first men to the Moon, these breakthroughs have transformed our lives. Casti illustrates each theorem with a dazzling array of real-world problems it has helped solve—how to calculate the shape of space, optimize investment returns, even chart the course of the development of organisms.

Along the way, we meet the leading thinkers of the day: John von Neumann, L. E. J. Brouwer, Marston Morse, and Alan Turing, among others. And we come to understand the combination of circumstances that led each to such revolutionary discoveries as the Minimax Theorem, which spawned the exciting field of game theory, and the Simplex Method, which underpins the powerful tools of optimization theory.

It has been estimated that about 200,000 theorems are published each year. How, then, does an author go about selecting a precious few as the most significant of the century? At the beginning of his search, Casti set forth five criteria: *Significance: Did the the

Most people have a very poor idea of what mathematicians do, since in school they are exposed only to centuries-old material. Casti (Complexification, HarperCollins, 1994) has written an excellent exposition of five of the most interesting mathematical theories of the 20th century that are still undergoing significant study. He discusses the mathematicians who discovered each theorem and explains how these theories are applied to real problems. This work is not for everyone; it is aimed at the nonmathematician willing to invest some time and effort to learn about modern mathematics. The serious reader will find it worth the effort; the chapter on "Theory of Communication" is in itself sufficient to recommend the purchase of the book.?Harold D. Shane, Baruch Coll., CUNY Copyright 1995 Cahners Business Information.