What will I learn about: how everyday mathematics acts as a workout for your brain, helping you make smarter daily decisions like comparing prices or finding the fastest commute?

Discover how everyday mathematics acts as a workout for your brain, helping you make smarter daily decisions like comparing prices or finding the fastest commute.

What will I learn about: why small sample sizes create misleading noise in data, and learn to gather comprehensive information to make truly accurate assessments?

Understand why small sample sizes create misleading noise in data, and learn to gather comprehensive information to make truly accurate assessments.

What will I learn about: Learn to stop seeing false patterns in random events by applying the null hypothesis and p-values to determine what is actually statistically significant?

Learn to stop seeing false patterns in random events by applying the null hypothesis and p-values to determine what is actually statistically significant.

What will I learn about: why big data cannot perfectly predict human behavior or chaotic events, helping you recognize the true boundaries of algorithmic models?

Find out why big data cannot perfectly predict human behavior or chaotic events, helping you recognize the true boundaries of algorithmic models.

What will I learn about: the crucial distinction between measurable risk and unpredictable uncertainty to better navigate and manage the complex choices you face?

Master the crucial distinction between measurable risk and unpredictable uncertainty to better navigate and manage the complex choices you face.

How Not to Be Wrong

The Hidden Maths of Everyday Life

Jordan Ellenberg

★ 4.1 / 5(144 ratings)

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Categories:

Science

If You're Curious About These Questions...

You should listen to this audiobook

💡Have you ever wondered why reinforcing the parts of a plane with the most bullet holes is actually the worst way to keep it from crashing?
💡What if you could master a hidden way of thinking that allows you to spot logical errors and misconceptions that most people miss?
💡Did you know that applying 'common sense' to complex problems often leads to the wrong answer, and there's a mathematical secret to finding the truth?

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Key Takeaways from How Not to Be Wrong

✓Discover how everyday mathematics acts as a workout for your brain, helping you make smarter daily decisions like comparing prices or finding the fastest commute.
✓Understand why small sample sizes create misleading noise in data, and learn to gather comprehensive information to make truly accurate assessments.
✓Learn to stop seeing false patterns in random events by applying the null hypothesis and p-values to determine what is actually statistically significant.
✓Find out why big data cannot perfectly predict human behavior or chaotic events, helping you recognize the true boundaries of algorithmic models.
✓Master the crucial distinction between measurable risk and unpredictable uncertainty to better navigate and manage the complex choices you face.

Learning Tools

Reinforce what you learned from How Not to Be Wrong

Mind Map

How Not to Be Wrong

Nature of Mathematics+

Linearity & Simplification+

Probability & Risk+

Statistics & Research Flaws+

Flaws in Public Opinion+

Quiz — Test Your Understanding

Question 1 of 8

During WWII, why did a mathematician suggest reinforcing the engines of returning planes rather than the fuselage, which had the most bullet holes?

A. The engines were cheaper and easier to reinforce than the fuselage.
B. The data suffered from survivorship bias; planes hit in the engine likely did not survive to be counted.
C. The fuselage was already heavily armored according to pre-war military specifications.
D. The enemy primarily targeted the fuselage, so adding armor there would make the planes too heavy.

Question 2 of 8

What is the primary purpose of using linear regression in statistics?

A. To connect every single data point accurately to form a complete and precise picture.
B. To eliminate all random 'noise' from observational data.
C. To simplify complex relationships into an approximation represented by a straight line.
D. To prove that two different variables have a direct, non-linear causal relationship.

Question 3 of 8

Why was the 2008 study published in Obesity, which claimed all Americans would be obese by 2048, mathematically flawed?

A. It applied linear regression to a long-term trend that is actually non-linear.
B. It used observational data from a sample size that was statistically insignificant.
C. It failed to establish a proper null hypothesis before testing the data.
D. It ignored the regression to the mean effect in long-term human dietary habits.

Question 4 of 8

What is the main limitation of relying solely on 'expected value' to make decisions about bets or investments?

A. It cannot be calculated for events with more than two possible outcomes.
B. It fails to account for the personal financial risk and the devastating impact of potential losses.
C. It inherently assumes that all outcomes have an equal probability of occurring.
D. It only applies to long-term scenarios and cannot be used to predict short-term gains.

Question 5 of 8

How does the 'regression effect' explain why a debut novelist's second book is often perceived as worse than their best-selling first book?

A. The author experiences exhaustion and naturally puts less effort into the second book.
B. The publisher provides less marketing support for the second book compared to the first.
C. An exceptionally successful first book is an unlikely extreme, so the next attempt will naturally tend to be closer to average.
D. Readers have artificially high expectations that cannot mathematically be measured or met.

Question 6 of 8

In statistical testing, what does it mean if a result achieves a p-value of less than 0.05?

A. The data proves the null hypothesis is exactly 95% likely to be true.
B. There is less than a 5% probability that the observed data came about by random chance.
C. The experiment needs to be repeated because the error rate is too high to be valid.
D. The variables being tested have a perfect linear relationship with zero noise.

Question 7 of 8

According to John Ioannidis, why do published research findings often present a distorted view of reality?

A. Scientists frequently falsify their data entirely to secure more government funding.
B. Most modern research instruments have too much random noise to ever be reliable.
C. Studies that fail to find significant results are rarely published, giving disproportionate attention to chance successes.
D. Researchers rely too heavily on the regression effect rather than utilizing linear regression.

Question 8 of 8

Why is the concept of a 'majority rules' public opinion often misleading when there are more than two options?

A. People generally refuse to answer polls that have more than two complex choices.
B. Different groups can be divided in ways that obscure the true preferences of the public, as seen in the 2000 US Election.
C. Pollsters usually manipulate the wording of the third option to intentionally confuse voters.
D. The statistical noise in multi-option polls makes calculating a p-value mathematically impossible.

How Not to Be Wrong — Full Chapter Overview

1Recommendation
21 — Mathematics is the science of avoiding mistakes, and it’s rooted in common sense.
32 — Linearity helps us simplify mathematical problems.
43 — Drawing conclusions from observational data can be unreliable, but probability theory can help.
54 — Probability theory shows what to expect from a bet, but risks still matter.
65 — The regression effect appears everywhere, though it often goes unnoticed.
76 — Linear regression is useful, but assuming linearity where it doesn’t exist can lead to false conclusions.
87 — Many research findings are flawed because data is misused or probability is calculated incorrectly.
98 — Polls and elections that claim to reflect “public opinion” are often wrong.
109 — Final summary

How Not to Be Wrong Summary & Overview

How Not to Be Wrong gives us an intimate glimpse into how mathematicians think and how we can benefit from their way of thinking. It also explains how easily we can be mistaken when we apply mathematical tools incorrectly, and gives advice on how we can instead find correct solutions.

Who Should Listen to How Not to Be Wrong?

Anyone interested in math
Anyone interested in logic or philosophy
Anyone interested in seeing the equations behind everyday situations

About the Author: Jordan Ellenberg

Jordan Ellenberg is a professor of mathematics at the University of Wisconsin-Madison. His work covers a wide variety of mathematical topics, including arithmetic geometry and number theory. Ellenberg writes the popular column, “Do the Math” for Slate, and has had work appear in The New York Times, the Washington Post and The Wall Street Journal. He is also the author of the novel Grasshopper King

How Not to Be Wrong

If You're Curious About These Questions...

Listen to How Not to Be Wrong — Free Audiobook

Key Takeaways from How Not to Be Wrong

Learning Tools

Mind Map

Quiz — Test Your Understanding

How Not to Be Wrong — Full Chapter Overview

How Not to Be Wrong Summary & Overview

Who Should Listen to How Not to Be Wrong?

About the Author: Jordan Ellenberg

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