-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 theorem break a major logjam in the development of mathematics?
  • BEAUTY AND SCOPE: Is the theorem elegant and does it shed light on questions over a wide range of areas?
  • APPLICATIONS: Do applications extend outside of pure mathematics and provide a more complete understanding of the workings of the world?
  • PROOF METHOD: Were new techniques or modes of logic required in the proof and did these methods provide insight into other important problems?
  • PHILOSOPHICAL IMPLICATIONS: Does the theorem provide opportunities to obtain deeper knowledge of ourselves and the universe?

One of the first books to focus exclusively on the mathematical breakthroughs of the 20th century, Five Golden Rules is wonderfully accessible, informative, and incisive.

JOHN L. CASTI is a resident member of the Santa Fe Institute and a professor at the Technical University of Vienna. He is the author of three previous trade books, Paradigms Lost, Searching for Certainty, and Complexification, as well as the two volume Reality Rules, a text on mathematical modeling.


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