Proving by day and disproving by night is not just for mathematics. I find it's a good habit to put pressure on all your beliefs, social, political, scientific, and philosophical. Believe whatever you believe by day; but at night, argue against the propositions you hold most dear. Don't cheat! To the greatest extent possible you have to think as though you believe what you don't believe. And if you can't talk yourself out of your existing beliefs, you'll know a lot more about why you believe what you believe. You'll have come a little closer to a proof."
"How Not To Be Wrong" is not a book about math. Well it is, but only if you first understand that math is not about memorization of the times table. It's about a way of logically thinking about the world. "How Not To Be Wrong" also happens to be another of Bill Gates's book recommendations for this summer.
After the jump, my review.
Jason Ellenberg is a professor of mathematics at the University of Wisconsin - Madison. I have some personal interest in that, having sat through many hours of mathematics courses in Van Vleck Hall at UW-Madison many decades ago. Ellenberg is also a regular columnist for Slate and other publications. This book has been adapted from that work. That origin shows, as the book moves from one mathematical topic to another, without any particular narrative arc.
"How Not To Be Wrong" covers topics such as the Laffer Curve, the Law of Large Numbers, the null hypothesis significance testing, regression to the mean, correlation vs causation, and non-Euclidean geometry. I use the technical terms only to warn potential readers that this book does deal with weighty subjects. Being able to comfortably handle concepts from algebra, geometry and statistics is required, even if you won't be required to solve any equations.
Let me balance that warning by saying that Ellenberg uses those concepts to explain everyday concerns of even non-mathematicians. Things like how to have fair elections when you have three candidates (hint: "majority rules" doesn't always lead to results most people consider right). Or why you should be skeptical when you read something like, "With current trends, everyone in America will be overweight by 2048." Ellenberg explains what's behind state rankings that show, for example, South Dakota leading the nation in brain cancer and North Dakota lagging (hint: moving across the state line probably won't keep you healthy). He also shows why you shouldn't be all that surprised when one person wins a lottery twice. He reveals your best strategy for making money playing Powerball. Choosing to play in the first place is almost always a poor choice, but millions of people do it anyway. Ellenberg explains why that says something worrisome about the foundation of much economics modeling.
So, if you are interested in learning how mathematics informs critical thinking about day-to-day concerns, that is, if you are interested in learning how not to be wrong, then I join Bill Gates in recommending this book for you.