Geniuses such as Beethoven or Einstein may be born creative, but creativity can be learned, practiced, and developed. Hence, it can also be taught. This book lays out a blueprint for teaching creativity, with a heavy emphasis on the areas of science, especially physics, usually taught at the undergraduate level. The aim is to develop insight and understanding rather than precision.

Creativity revolves around three main ideas: the ability to think and perceive in new and different ways, a skill often called lateral thinking; the ability to use both sides of the brain cooperatively, the linear, verbal left brain along with the intuitive, nonverbal right brain; and the ability to generate, evaluate, and filter alternatives. In section 1.7, “Talking to Your Gut,” Mahajan proposes a nifty procedure to hold a dialog between your left brain and your right brain, namely to have your left brain propose ideas, and to listen to the right brain’s responses expressed as feelings of comfort or discomfort. Since both sides of the brain store vast amounts of knowledge, the task is to tap that knowledge without favoring one side of the brain or the other.

The emphasis of the book, however, is on techniques to generate solutions to physical problems. The techniques are grouped around three themes: organizing complexity, discarding complexity without losing information, and discarding complexity with loss of information. The layout of the book is as follows: Part 1, “Organizing Complexity,” includes chapter 1, “Divide and Conquer,” and chapter 2, “Abstraction.” Part 2, “Discarding Complexity Without Losing Information,” includes chapter 3, “Symmetry and Conservation”; chapter 4, “Proportional Reasoning”; and chapter 5, “Dimensions.” Part 3, “Discarding Complexity with Loss of Information,” includes chapter 6, “Lumping”; chapter 7, “Probabilistic Reasoning”; chapter 8, “Easy Cases”; and chapter 9, “Spring Models.”

While computer scientists can easily relate to some topics (divide-and-conquer, approximation, symmetry, random walks, probabilistic reasoning), the book is meant for engineers more than for computer scientists or mathematicians. The techniques shown, and the numerous exercises included, concentrate on understanding engineering problems in novel ways and reaching approximate solutions. This approach is prefigured by the inclusion, on page xvii, of physical constant values that can be used for back-of-the-envelope calculations. And, while generalization and abstraction provides an underlying foundation throughout, mathematics is used as a tool, so developing and nurturing mathematical thinking is not treated systematically.

Corrado Mencar’s excellent review (CR143418) gives another perspective on the contents of the book. I also would like to add a couple of observations:

The literature on creativity and innovation is very large. Mahajan’s 50-entry bibliography is highly varied and selective. Surprisingly, it does not include a classic masterpiece about mathematical creativity, G. Polya’s Mathematics and plausible reasoning, published in two volumes by Princeton University Press in 1954 and recently reissued by Martino Publishing as a single, inexpensive paperback volume [1]. I recommend this work without hesitation not only to mathematicians and computer scientists, but also to anyone interested in the art of problem solving.

This book makes for interesting reading. You can certainly treat it as a serious book, but you could also treat it as the kind of book you can read for pleasure and at leisure while on vacation. It has lots of problems you can work on as interest or time allows, or when you want to put insomnia to good use. However, neither hints nor solutions are provided. Finally, keep in mind that in the world of business, science, or engineering, once you gain insight and understanding, you will need to come up with an exact solution.

This book will be particularly useful to young scientists and engineers. For some readers, it can be of lasting value.

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