How Not to Be Wrong: The Power of Mathematical Thinking

Jordan Ellenberg is one of the rare university professors who also publishes prodigiously for the public. Much of his writing comes together in his book, How Not to Be Wrong. A collection of mathematical history, practice, and theory, the book is engaging and provocative. Ellenberg’s writing style allows him to present a seemingly bland topic in an approachable manner. Even when the theory left me scratching my head, Ellenberg kept my attention. Seeking to redeem mathematics from its too often bland or negative reputation, the title’s promise is part of a larger goal: Demonstrate the hidden mathematical thinking we often assume as common sense.

We tend to teach mathematics as a long list of rules. You learn them in order and you have to obey them because if you don’t obey them you get a C-. This is not mathematics. (12)

You may not be aiming for a mathematically oriented career. That’s fine—most people aren’t. But you can still do math. You probably already are doing math, even if you don’t call it that. Math is woven into the way we reason. And math makes you better at things. (2)

Provocative premises drive his fascinating examples, like “Why South Dakota has more brain cancer than North Dakota.” Ellenberg covers basic principles like probability and statistics, while delving into the history and theory behind them. Though each chapter covers various mathematical concepts, the overarching argument that math empowers you to make better decisions (even if that includes saying “I’m not sure”) convincingly connects each section.

But real-world questions aren’t like word problems. A real-world problem is something like “Has the recession and its aftermath been especially bad for women in the workforce, and if so, to what extent is this the result of Obama administration policies?” Your calculator doesn’t have a button for this. Because in order to give a sensible answer, you need to know more than just numbers…Dividing one number by another is mere computation; figuring out what you should divide by what is mathematics. (85)

As a current academic and college professor, Ellenberg pulls back the curtain of contemporary mathematics. This behind-the-scenes view is a nice bonus for the reader. It also serves to humanize himself and other academics, another way to remove some of the intellectual intimidation that mathematics, particularly advanced math, brings.

One of the most painful parts of teaching mathematics is seeing students damaged by the cult of the genius. The genius cult tells students it’s not worth doing mathematics unless you’re the best at mathematics, because those special few are the only one whose contributions matter. We don’t treat any other subject that way! (412)

I wouldn’t call How Not to Be Wrong a light read, but it’s engaging and interesting for even the non-self-described math nerd. Ellenberg makes mathematical concepts understandable and is worth a read if you’re looking to learn something from your next read.

How Not to Be Wrong: The Power of Mathematical Thinking

Next time: Malcolm Gladwell’s Revisionist History

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