[7][8] Ellenberg uses mathematics to examine real-world issues ranging from the loving of straight lines in the reporting of obesity to the game theory of missing flights, from the relevance to digestion of regression to the mean to the counter-intuitive Berkson's paradox.

[10] Chapter 4, How Many Is That In Dead Americans: Ellenberg analyzes statistics about the number of casualties around the world in different countries resulting from war.

To support this, he uses examples about hidden codes in the Torah determined by Equidistant Letter Sequence, a stockbroker parable, noting that "improbable things happen", and wiggle room attributes to that.

These include but aren't limited to the Reductio Ad Absurdum by Aristotle, a look into the constellation Taurus by John Mitchell, and Yitang "Tom" Zhang's "bounded gaps" conjecture.

It's Me, Bayesian Inference: This chapter relates algorithms to things ranging from God, to Netflix movie recommendations, and to terrorism on Facebook.

Many mathematicians and other famous people are mentioned in this chapter, including Georges-Louis Leclerc, Comte de Buffon, and James Harvey.

This chapter discusses the amount of time spent in the airport as it relates to flights being missed, Daniel Ellsberg, Blaise Pascal's Pense's, the probability of God once more, and the St. Petersburg paradox.

It uses many examples to make its point, including different election statistics, the death sentence of a mentally retarded person, and a case with Justice Antonin Scalia.

It also includes mathematical terms/concepts such as independence of irrelevant alternatives, asymmetric domination effect, Australia's single transferable vote, and Condorcet paradoxes.

"[19] The Wall Street Journal said, "Mr. Ellenberg writes, a kind of 'X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.

"[21] Business Insider said it's "A collection of fascinating examples of math and its surprising applications...How Not To Be Wrong is full of interesting and weird mathematical tools and observations".

[22] Publishers Weekly writes "Wry, accessible, and entertaining... Ellenberg finds the common-sense math at work in the every day world, and his vivid examples and clear descriptions show how 'math is woven into the way we reason'".

[23] Times Higher Education notes "How Not To Be Wrong is beautifully written, holding the reader's attention throughout with well-chosen material, illuminating exposition, wit, and helpful examples...Ellenberg shares Gardner's remarkable ability to write clearly and entertainingly, bringing in deep mathematical ideas without the reader registering their difficulty".