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How Not to Be Wrong
The Power of Mathematical Thinking
By Jordan Ellenberg
2014, Penguin Press

How Not to Be Wrong is a brief introduction to mathematics as it relates to critical thinking. It focuses less on numbers and operations, and more on logical structures, improved statistical thinking, and advanced common sense.

The subject matter is diverse and wide-ranging, and a brief summary is not practical. Ellenberg covers cognitive biases such as the survivorship bias and counterintuitive effects such as regression towards the mean. He explains P values and confidence intervals, errors of statistical and probabilistic thinking. He touches on how to fix democracy and how to beat the lottery... and much more, all with real-world examples interspersed with interesting bits of history.

This book is somewhat misrepresented; the back cover advertises it as the Freakonomics of math. However, the hallmark of Freakonomics was that it presented some interesting new ideas. Jordan Ellenberg is perhaps more akin to the Malcolm Gladwell of math, presenting interesting but old ideas in an accessible way, with relevant anecdotes and lots of connections to make the information more meaningful to non-experts.

How Not to Be Wrong is a good intermediate book for people interested in critical thinking and mathematics. It contains enough technical information, and covers enough ground, that I expect it would also be enjoyed by the majority of math majors, and it isn't so technical that the average reader will often feel confused (he lost me briefly when talking about the geometry of perspective, but I recovered quickly). Most importantly it reviews a lot of important ideas that support critical thinking across domains, making it a good resource for anyone who wants to not be wrong. Regardless of your opinion on math in general, I recommend giving this book a try.

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