How Not to Be Wrong

How Not to Be Wrong explains the mathematics behind some of simplest day-to-day thinking. It then goes into more complex decisions people make. For example, Ellenberg explains many misconceptions about lotteries and whether or not they can be mathematically beaten. 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. == Chapter summaries ==

Part 1: Linearity Chapter 1, Less Like Sweden: Ellenberg encourages his readers to think nonlinearly, and know that "where you should go depends on where you are". To develop his thought, he relates this to Voodoo economics and the Laffer curve of taxation. Although there are few numbers in this chapter, the point is that the overall concept still ties back to mathematical thinking. Chapter 2, Straight Locally, Curved Globally: This chapter puts an emphasis on recognizing that "not every curve is a straight line", and makes reference to multiple mathematical concepts including the Pythagorean theorem, the derivation of Pi, Zeno's paradox, and non-standard analysis. Chapter 7, Dead Fish Don't Read Minds: This chapter touches on a lot of things. The basis for this chapter are stories about a dead salmon's MRI, trial and error in algebra, birth control statistics, alliteration in Shakespeare, and basketball statistics (the "hot hand"). Additionally, he writes of a few other mathematical concepts, including the Null hypothesis and the Quartic function. He explains how underpowered statistical studies can lead to misleading results, especially when the result given by the null hypothesis is close to the result gotten by rejecting it. Chapter 12, Miss More Planes: The mathematical concepts in this chapter include utility and utils, and the Laffer curve again. This chapter discusses the amount of time spent in the airport as it relates to flights being missed, Daniel Ellsberg, Blaise Pascal's Pensées, the probability of God once more, and the St. Petersburg paradox. Chapter 15, Galton's Ellipse: This chapter focuses on Sir Francis Galton, and his work on scatter plots, as well as the ellipses formed by them, correlation and causation, and the development from linear systems to quadratics. This chapter also addressed conditional and unconditional expectation, regression to the mean, eccentricity, bivariate normal distribution, and dimensions in geometry. Chapter 18, "Out of Nothing, I Have Created a Strange New Universe": This chapter talks about János Bolyais, and his work on the parallel postulate. Others mentioned in this chapter include David Hilbert, and Gottlob Frege. It also explored points and lines, Formalism, and what the author calls a "Genius" mentality. == Reception ==

The Washington Post reported that the book is "brilliantly engaging... part of the sheer intellectual joy of the book is watching the author leap nimbly from topic to topic, comparing slime molds to the Bush–Gore Florida vote, criminology to Beethoven's Ninth Symphony. The final effect is of one enormous mosaic unified by mathematics." 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." The Guardian wrote, "Ellenberg's prose is a delight – informal and robust, irreverent yet serious." 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". 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'". 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". Salon describes the book as "A poet-mathematician offers an empowering and entertaining primer for the age of Big Data...A rewarding popular math book for just about anyone". Bill Gates endorsed How Not to Be Wrong and included it in his 2016 "5 Books to Read This Summer" list. == References ==