How Not to Be Wrong
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3:16What is How Not to Be Wrong about?
Mathematician Jordan Ellenberg argues math is not a distant technical subject but common sense sharpened, an extension of everyday reasoning. Through stories from lottery schemes to wartime armor placement, he shows how linear thinking, misread statistics, and misunderstanding of inference lead smart people astray, and how mathematical thinking corrects course.
Key ideas from How Not to Be Wrong
Survivorship Bias
Ellenberg opens with Abraham Wald, who told the military to armor bombers where returning planes had no bullet holes, since planes hit there never came back. The data you see is filtered by what survived to be seen.
Not Everything Is Linear
Assuming trends continue in straight lines produces absurdities, like projecting that all Americans will be obese by a given date. Many relationships curve, so more is better only up to a point, then it reverses.
Improbable Is Not Impossible
With millions of trials, someone will win the lottery twice and some study will hit statistical significance by luck. Ellenberg dissects p-values and regression to the mean to show why headlines routinely mistake noise for miracles.
Lines worth keeping
- Mathematics is mostly the discipline of noticing which obvious next step is actually a trap.
- If you torture enough data, some coincidence will always confess, and the newspapers will print it.
Is How Not to Be Wrong worth reading?
Read it fully if you want to genuinely upgrade your reasoning about statistics, studies, and headlines, since Ellenberg is funny, rigorous, and honest about uncertainty. The middle chapters on expected value and geometry demand patience, and readers wanting quick takeaways may prefer a tighter book. As numeracy training disguised as entertainment, it is hard to beat.
Jordan Ellenberg · 2014 · Science & Big Ideas · Distilshelf editorial · Updated August 2026