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*Mathematics: Powerful Patterns in Nature and Society,* by Harry Henderson, 2007, 170 pages, hardcover $35, ISBN: 0-8160-5750-4, Chelsea House Publishers, www.chelseahouse.com.

Humans have always used observations of patterns to help mankind survive with a better understanding of the world in which we live. This book is another volume in the Milestones in Discovery and Invention series and will give the reader an overview of the studies and research of patterns that have been conducted in the past as well as what is happening currently in the field.. Most of the ten scientists/mathematicians spotlighted lived during the 20th century and some are still living today. Many of these pattern-finders liked solving puzzles and playing games as a youngster. Interview quotes from a variety of sources from these avant-garde thinkers and from those who worked with them or knew them give an intriguing insight into their minds. Some of these patterns seemed to have only recreational value when first discovered, but they have been shown to be valuable tools in describing weather systems, economic behaviors, and biological interactions. The artificial life and artificial intelligence systems use computer programs that allow the system to “evolve” based on interactions within the system. This is in direct contrast with traditional explicit models that use equations to describe past behavior and make future predictions.

The titles of the ten chapters of Mathematics: Powerful Patterns in Nature and Society are as follows:

- How Nature Counts: Leonardo of Pisa Discovers Fibonacci Numbers
- Tools for Pattern-Finders: Karl Pearson and Statistics
- Surmises and Simulations: John von Neumann Puts the Computer in Play
- A Delicate Equilibrium: John Nash and Game Theory
- Endless Structure: Benoit Mandelbrot Opens the Fractal Portal
- On Butterfly Wings: Edward Lorenz and Chaos Theory
- Games of Emergence: John H. Conway, “Life,” and Other Pastimes
- From Cosmos to Mind: Roger Penrose Suggests Hidden Connections
- Artificial Evolution: Christopher Langton Creates Virtual Life
- A New Kind of Science? Stephen Wolfram and the Universal Automaton

Each chapter begins with the influences that set the person on his path to discovery and ends with a chronology of the person’s life and suggestions for further reading in books, articles, and websites. Written in layman’s terms, this book might inspire some in our younger generation to pursue similar studies of patterns. With global warming threatening our existence, we need to encourage young scientists and mathematicians to engage in studies that will help find solutions to our predicament. Middle and high school libraries should have the Milestones in Discovery and Invention series on display and teachers should encourage students who may be interested in these fields to read these books.

Linda Y. Shuey, Teacher, Western Albemarle H.S., Crozet, VA

Linda Y. Shuey, reviewer, "Mathematics: Powerful Patterns in Nature and Society," *Convergence* (October 2007)