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What it argues
Jordan Ellenberg is a research mathematician who writes as if mathematics is something you would want to think about over dinner. This book is his argument that mathematical thinking — not calculus or algebra, but the underlying habits of reasoning that mathematics trains — is one of the most powerful tools available for navigating ordinary life. The title is deliberately modest. Ellenberg isn't promising to make you right; he's promising to make you less systematically wrong.
The book ranges across a dozen mathematical ideas: the geometry of straight lines and why linear models mislead us, the expected value of lotteries and why people consistently play them wrong, the properties of regression to the mean and how they produce false impressions of causation, the mathematics of voting and why no voting system can satisfy all reasonable criteria simultaneously, and the logic of hypothesis testing and why most published findings are statistically weaker than they appear. Each topic is developed through stories rather than formulas, from the U.S. lottery that was briefly profitable to Abraham Wald's famous analysis of where to armor bullet-damaged planes.
What it gets right
- 1.
Linear reasoning fails outside its range. Many phenomena are linear locally but curve dramatically at the extremes, and applying a linear model past its valid range produces absurd predictions.
- 2.
Survivor bias distorts nearly every domain where you only observe what succeeded. Abraham Wald's plane-armor analysis is the classic case, and the pattern appears everywhere from investment funds to startup advice.
- 3.
Regression to the mean is automatic and impersonal. Extreme performances tend to be followed by more average ones regardless of what you did between them — which produces false impressions of causation.
What it covers
Who wrote it
Jordan Ellenberg is a professor of mathematics at the University of Wisconsin–Madison, where he holds the John D. MacArthur Chair. His research spans number theory, algebraic geometry, and combinatorics. He has written on mathematics for Slate, the Wall Street Journal, the New York Times, and other publications, and he was a National Magazine Award finalist. He is also the author of Shape (2021), which applies geometric thinking to networks, data, and maps.
