Saturday, July 28, 2018

How Not To Be Wrong: a very short review

I'm a sucker for popular mathematics books.

Especially good ones.

Jordan Ellenberg's How Not to Be Wrong: The Power of Mathematical Thinking is a good popular mathematics book.

Although the book is wide-ranging, with many interesting topics, two particularly stand out to me.

The first is the strong treatment of the notion of "statistically significant." Ellenberg explores this notion in a number of ways, looking at ways in which it is used (correctly and incorrectly), what it means to say something is statistically significant, rigorously, and even looks at the historical background of statistical significance, tracing it back to John Arbuthnot in the late 17th century.

The second, much more entertaining if maybe not as practically useful, is Ellenberg's detailed and fascinating exploration of modern state lotteries, and how they fail. In particular, he looks at the flawed Cash WinFall lottery that was held in Massachusetts in the early 2000's, and how various parties (university students, actuaries, lottery hobbyists, etc.) found errors in the lottery rules that enabled players to profit from the lottery if they did things just right. The mathematical underpinnings here involve the notion of "expected value," and Ellenberg's treatment is extremely interesting.

If you like popular mathematics, you'll enjoy How Not to Be Wrong: The Power of Mathematical Thinking

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