To me, the most intriguing aspect of this book was Professor Paulos's ability to take simple math concepts that I learned way back when . . . and to show how they could enrich and expand my appreciation of the world around me now. It was like Alice going through the looking glass in the sequel to Alice in Wonderland. There's a lot there that I never imagined. For example, the way disease rates are often described is for those who have survived to 85 years old. If you are younger, your current probability of incidence will be much lower (possibly more than 90 percent lower). Also, you can use the way you design your questions and sample to help eliminate bias (such as by asking about the results of a coin flip and dangerous sexual behavior in the same population). You can also find great humor in the errors of authority figures who misquote probabilities and risks. Plus, you can answer questions that I would never have thought of (such as the likelihood of breathing in an atom that Caesar did).
If you are feeling cowed about your math ability, take heart! Most of the concepts here you can handle. For example, can you multiply two numbers together? You can answer "yes" to my question if you can do so with a calculator. If so, you can appreciate almost all of the examples in the book.
Professor Paulos has a mind that works differently and more inquisitively from mine, but I enjoyed learning how his thoughts. He thinks about topics like how long it would take dump trucks to excavate Mount Fuji, how many times a deck of cards need to be shuffled to become random, and what the Earned Run Average is for a pitcher who lasts one-third inning and gives up 5 runs. I realized that if I thought about more things like this, I would develop new perspectives on the world.
He makes a helpful attempt to create solutions so that more people can appreciate the world in a quantitative sense. These include using exponents to indicate the size of numbers (such as the Richter Scale does for earthquake strength), refocusing secondary math education to practical applications rather than teaching calculus earlier and earlier, having talented mathematicians teach younger people, and disciplining those who communicate in public to check the mathematical accuracy of what they say.
What do we lose if we don't? Well, those who don't learn a little math will end up in careers that pay a lot less. Social resources will be misapplied to problems that are less serious (obscure diseases and terrorism get a lot more attention to reducing accidental deaths among young people, which is a greater danger). We will make bad resource decisions in our own lives (such as by playing the lottery without realizing that 50% of the money is not paid out to anyone buying a ticket).
I also appreciated how few people can use mathematics in creative ways, to solve problems. For instance, in our professional practice we developed a new way to forecast certain forms of investment behavior. Over 20 years of doing this work, I have never found anyone who could make a single useful suggestion for how to improve the mathematics of our approach, despite having had conversations with dozens of people with advanced math and statistics degrees who would get benefit from an improved approach. I suspect from this experience that there's a higher level of mathematical thinking that Professor Paulos did not explain in his book that we would all benefit from learning. Where do we start? I can hardly wait to learn!