Magnificent Mistakes in Mathematics, by Alfred S. Posamentier and Ingmar Lehmann, is pretty much what the title suggests. This book discusses the role of math in our culture and how some of the most well known theories have been found to have flaws.
For example, most readers will be familiar with pi. It starts out 3.14 etc. William Shanks took fifteen years to figure out its value to more than a few decimal places. In recognition of this achievement, the Palais de la Decouverte in Paris decided to reproduce the number in order to decorate a cupola. However, it took a calculator running for nearly three days before the mistake ended up caught. Five hundred and twenty seven numbers which followed the three were fine. It was the next number which required correcting.
Triangles have three sides and three angles. For one to suggest every triangle is isosceles means a violation of the concept of betweeness. Euclid could not have recognized this idea when he was alive and creating mathematical formulas still used today.
While one might be inclined to believe a math flaw is cause for concern, Posamentier and Lehman suggest a completely different idea. Sometimes, in attempting to uncover how to fix an error, new concepts are discovered.
At least one error is easily recognizable. Enrico Fermi made a mistake in a formula simply by switching two symbols so each ended up in the other’s place. The problem was made a bit worse after a photograph of the error ended up on a postage stamp in 2001.
Readers are not actually required to know much about math to understand the concepts presented in this book. If they took a few courses in high school, it is enough. Each theory is presented in clear, easy to understand terms.
There might be some ambitious souls who wish to try out the formulas for themselves. Included are processes to work these out on paper. Some common mistakes are discussed, in case the answer does not quite work out as the authors intended.