Published in April 2008 by Harper Collins, Stein’s first solo effort reveals how seemingly arcane mathematical investigations and discoveries have led to insights into why the things that work well do so – and why the things that don’t work well screw up. Refrigerators, computers and jet planes work remarkably well, thanks in part to our understanding of the mathematical physics that underlie these technologies. However, we are far less successful at designing systems to plan and predict. It rains when we use the weather forecast to plan a picnic, and somehow, the airline managed to send our luggage to Cleveland. These failures are not always due to the inevitable human error, but to the fact that some problems are so intrinsically difficult that we may not be able to solve them.
Part of the beauty of mathematics is that it can be used to explain phenomena that range from the sublime – such as the true nature of space and time – to the annoyingly ordinary, such as why your car is never ready at the time the garage said it would be. Some of the book focuses on three of the great mathematical discoveries of the 20th century that represent some of the limits of what we cannot know or do. The Heisenberg Uncertainty Principle demonstrates that we cannot know everything about the physical universe. Gödel’s Incompleteness Theorem shows that there are mathematical truths that logic cannot establish. Finally, Arrow’s Impossibility Theorem reveals that there is no perfect way to determine the winner of an election.
The book is not just a recitation of the results; it is also the stories of the people who established them and the times in which they lived. Mathematics may exist in the abstract, but it takes human beings to discover it, and sometimes their stories are every bit as interesting as their discoveries.
“The book is for an intelligent reader who is curious about things,” Stein said. “We can’t know everything. We can’t accomplish everything. We live in a world where people continually delude themselves. So it’s important for us to know what is possible and what is impossible. If something is not possible, it is important to figure out what is possible and the best way to do it. That is the task of mathematics.”
Stein earned his bachelor of arts from Yale in 1962 and his master’s and Ph.D. from Berkeley in 1967. He currently lives in Redondo Beach with his wife Linda. His current interests are tennis and piano, and he claims that he has finally shaken the addiction to duplicate bridge that caused his thesis advisor to despair of his ever obtaining a degree.