Book Review: How Not to Be Wrong

January 20, 2020

Cover: How Not to Be WrongThere are certain topics—politics, religion, sex—that are sure to invite disagreement, judgment, and the gnashing of teeth. I want to add math education to that list of uncomfortable discussion topics. Math education—how math is taught and whether it is really applicable to the real world—as been a consistent source of irritation for parents and students across generations.

When I was in school, I hated math. In fact, I maneuvered my education so I could take my final math class in the 11th grade—meeting the state’s minimum requirements for high school. I avoided math throughout my post-secondary education, but I was still able to earn undergraduate and graduate degrees. Nearly 20 years after that final math class, in an admission interview for business school, I shared that I was somewhat concerned about the accounting, finance, options, and statistics courses I would need to take. The admissions committee assured me that I would do fine.

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As Jordan Ellenberg, the author of How Not to Be Wrong, describes in his book, students tend to become alienated from math at two points in their math journey. The first of these points occurs at the introduction of fractions in primary school. It is challenging for students to understand the difference between natural, or counting, numbers and the more complex constructs that describe proportions and relationships. The second point that tends to lead to mathematical disinterest is the introduction of algebra. Ellenberg hypothesizes that algebra—which is an exercise in reverse engineering a formula—becomes tedious and confusing. Before the introduction of algebra, math is a straightforward, algorithmic exercise. For me, the introduction of algebra was mind numbing. My math teachers told me that math was important in engineering and in building our world, but what I saw was a system that seemed to reject creativity and divergent thought.

I recall, with great clarity, my 7th-grade math teacher stating that his method for solving equations as “the only way” to solve problems. To the middle-school version of myself, it seemed impossible that, given the rigidity of math, it could have applications in engineering, architecture, and other creative ventures.

To my surprise, I actually ended up liking math when I was in business school. I discovered that are many applications for math and its related skills. Even though I have no expectation of becoming a great mathematician, I do appreciate the use of math to support decision-making and forecast future outcomes with greater precision than my gut feelings allow.

Book Specifications

Title: How Not to Be Wrong: The Power of Mathematical Thinking

Author: Jordan Ellenberg

Formats: Paperback, hardcover, and Kindle

Publisher: Penguin Books

Published: May 26, 2015, Reprint edition

Pages: 480

ISBN-10: 0143127535

ISBN-13: 978-0143127536

Numbers Don’t Lie, but Statisticians Politicians Do

A central theme of Ellenberg’s book is that people should embrace mathematical literacy so they cannot be deceived when those in authority present numbers to them—be they the media, politicians, financial advisors, or others. Frequently, people assume that numbers are accurate without checking the math. Even if we do check the arithmetic, it is still possible to get bad information because of our limited perspective on the data.

Ellenberg provides a wonderful example: In June 2011, the U.S. Bureau of Labor Statistics released a report showing anemic job growth of only 18,000 jobs. That was not good news, but the governor of Wisconsin was heartened to see—and likely overjoyed to claim in a news release—that his state accounted for more than 50% of the national jobs growth in the U.S., with 9,500 new jobs. While that could be possible, this information should inspire closer examination because we know that Wisconsin is just one of 50 states and is not among the most populous states. After reviewing the data, It was clear that Minnesota had also added 13,000 jobs during the same period. How could this be? Minnesota’s 13,000 jobs plus Wisconsin’s 9,500 jobs added up to more new jobs than the entire U.S. economy added during that period.

This is the point at which people might realize that the data was cherry-picked to support a predetermined narrative. While it might have been true that these states added jobs, the Wisconsin governor’s claim conveniently omitted the churn—jobs that the state lost during the same period. Not counting negative numbers is a fundamental error in representing information.  This example becomes especially important as we consider accountability for investments, employees, and politicians.

Things Go on Forever

Ellenberg’s metaphors bring humor to his explanations of complex mathematical concepts. Human bias is toward thinking linearly—that is, assuming a current state or growth at the same rate would continue. For example, as Ellenberg wonders in his book: Can we predict the location of a ballistic missile? Knowing its direction and speed, yes. It is very easy to determine its location. However, missiles don’t move in one direction forever. Engineers design them to turn and land back on earth, preferably some distance from their launch point. This behavior introduces new variables such as gravity and wind resistance. This is one of the best explanations of calculus I’ve read—accounting for factors that determine the value of variables under certain conditions. It’s also a practical application of math.

In a similar vein as his denial of the example of the missile that flies in a straight line forever, Ellenberg critiques a national health study that claimed, by 2048, 100% of Americans would be obese. This is a fairly significant claim that would be sure to get headlines. But again, when we look into the numbers and the regression analysis that the study provided, we see significant problems. For example, the document uses a crude, linear analysis of the data to arrive at its conclusion, which indicates that, by 2060, around 109% of Americans would be obese. As the author notes, the paper includes further errors, indicating that black American males are becoming obese at half the rate of the overall population, so it would not be until 2095 that 100% of black American males would have become obese. But none of this is plausible. The root of the problem is that the report’s authors failed to consider the curve. Rates would slow over time, so the underlying statistical analysis falls apart fairly quickly.

You don’t need to do any complex math to realize that there are some logical contradictions in this example. We should probably be skeptical of these sorts of claims.

Commonplace Improbability

The problem of not knowing where we are in a series of events encourages people to make bad decisions every day. We have a tendency to assume that current states of being will continue. People buy into the stock market with enthusiasm when the market is up, invest in companies that are outperforming the market, bet on basketball players who have a hot-hand, bet on numbers that haven’t won recently on roulette wheels, and create algorithms that trick them into believing there are coded messages in the Torah—otherwise known as “The Bible Code.” People try to find patterns in their environment to make sense of things or to find an advantage. But we deceive ourselves by assuming that unrelated events have some bearing on each other.

Ellenberg uses the example of coin flipping to describe the problem of small samples. While we can assume that flipping a fair quarter in the air would result in a 50% chance of the quarter’s landing heads up, this does not mean that two coin flips would result in an equal distribution of heads and tails. Likewise, seeing a coin flip land five times in a row does not mean the sixth flip would land tails up. However, an appropriate sample size—perhaps 100 flips—would be likely to follow our assumption of an equal distribution of heads and tails.

Understanding the rationale and applicability for sample sizes is critical for UX professionals who conduct surveys or analyze large data sets.

Word Problems

Perhaps one of the most challenging aspects of math education relates to word problems. Performing simple—or even complex—mathematical calculations might be relatively simple for most people, but solving word problems is where the idea of mathematical thinking really shines. To be able to successfully solve a word problem, people must identify the relevant factors that support a decision. It is in solving word problems that we truly put our cognitive ability to the test.

While word problems can be challenging, the truth is that virtually all applications of math in the real world are math problems that are just waiting to be articulated.


Although you might assume that this is a book about math, it does not include a particularly heavy amount of arithmetic. Instead, Ellenberg presents mathematical tactics for testing our assumptions. This book encourages divergent thought, while providing tools that promote confidence. It also provides several thought-provoking examples, with analysis that encourages readers to think critically about the logic of our decisions, as well as the information that organizations provide to us.

Although this is not a typical UX book, Ellenberg does discuss how to understand A/B testing in a rational way. Nevertheless, when we, as UX professionals, need to make sound decisions and assess the quality of our assumptions, the tools of mathematical thinking can be invaluable. 

Owner and Principal Consultant at Covalent Studio LLC

Akron, Ohio, USA

D. Ben WoodsBen’s global design and technology firm specializes in software design and development for the Web, mobile, and ecommerce. The company serves clients ranging from small startups to some of the largest companies in the world, including General Electric, Rio Tinto, and Fidelity. His career in User Experience began in the late 1990s. Ben has held diverse roles, including UX management at a global B2B firm, full-time and part-time academia, and executive roles. He enjoys solving complex business problems and coaching talent to be competitive UX design professionals. Ben earned his MS in Information Architecture and Knowledge Management at Kent State University and is a graduate of the Executive MBA program at Case Western Reserve University’s Weatherhead School of Management. He has presented long-format talks, speed presentations, and posters at many conferences and events and has conducted training and workshops for organizations throughout the United States, Europe, and Asia.  Read More

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