Review of ‘Magnificent Mistakes in Mathematics’
Magnificent Mistakes in Mathematics
By Alfred S. Posamentier and Ingmar Lehmann
Published by Prometheus Books, Amherst, NY. 2013: 296 pp.
Given my uncomfortable relationship with math and math classes, where the idea of “mistakes” haunted nearly every experience I had, I’ll admit that I approached this particular assignment with dread and a knot in my stomach.
If math and mistakes conjured an unpleasant memory of suffering through too many “gotcha” moments in those long-ago high school geometry and trigonometry classes — pre-calculator —, I soon realized that the authors had a different intention. Posamentier, dean of the School of Education and professor of mathematics education at Mercy College and Ingmar Lehmann, who retired from the mathematics faculty at Humboldt University in Berlin, are very much about math as a delightful intellectual exercise that enhances critical thinking across all disciplines.
As they write, “our objective in this book is to entertain the reader with a collection of wrong conclusions — or fallacies — that help us to better understand important aspects of or concepts in mathematics …. Yet it is the unique value of these mistakes — providing a better understanding of the basic concepts of mathematics — that makes these mistakes magnificent. Lest we forget, youngsters — and, we dare say, adults as well — learn quite a bit from mistakes.” In fact, many of these mistakes, and the efforts to unpack them, have led to a more nuanced understanding of math and, frequently, profound new discoveries.
The reader should be able to draw consolation from some of the major whoppers made by some of the greatest mathematical minds. Consider that Galileo, examining a ball’s travel along a polygonal path, thought that the arc of a circle would be the fastest curve for a ball to travel, rather than a straight line — except that he didn’t take into account that polygon sides do not necessarily have the same length. Albert Einstein’s mistakes have inspired entire books.
Some errors in arithmetic illuminate the practical consequences of what appears to be a correct mathematical answer. Suppose that students are asked to do a rounding problem, to find out how many buses would be needed to transport 963 stranded passengers at an airport. Each bus can hold 59 people. Students who, correctly, round the answer to the nearest whole number — 16, from an answer of 16.322 — would end up leaving passengers stuck at the airport.
Then there’s the so-called Monty Hall problem, based on the strategy needed to select the correct door on the game show, Let’s Make a Deal; contestants’ choice of the “likely” versus “unlikely” door was often based on a mistaken understanding of probability.
By the time I got to the sections on coin tosses and dice, I was actually enjoying myself.
I’ll confess that this volume is more likely to appeal to people like my husband and his fellow Stuyvesant math teammates than unrepentant math-phobics like myself. Still, it would undoubtedly be a great addition to the classroom shelves of math teachers, who could offer particular problems and examples to some of their more gifted students, as a way to challenge and expand their mathematical minds. #