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How Not to Be Wrong summary

The Hidden Maths of Everyday Life

4.1 (135 ratings)
20 mins

Brief summary

How Not to Be Wrong by Jordan Ellenberg is a book that explores how mathematics can aid in better decision-making. It shows how math is integrated into our daily lives, making complex concepts simpler and transforming the way we think about the world.

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    How Not to Be Wrong
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    Mathematics is the science of not being wrong, and it's based on common sense.

    Convoluted mathematical formulas you encountered in school might have made your head spin. At the time, you might have asked yourself, “Will I ever use this in real life?”

    The short answer is yes. Math is a key tool in solving common problems. We all use math every day, but we don't always call it “math.”

    In essence, mathematics is the science of not being wrong.

    Consider this example: During World War II, American planes returned from tours in Europe covered in bullet holes. Curiously, a plane’s fuselage always had more bullet holes than did the engine.

    To better protect the planes, military advisors suggested outfitting the fuselage with better armor. One young mathematician suggested instead improving the armor for the engine.

    Why? He suspected that those planes that took shots to the engine were actually those that didn’t make it back. If the engines were reinforced with better armor, more planes might survive.

    There's a mathematical phenomenon known as survivorship bias underlying this situation. Survivorship bias is the logical error of concentrating on the things that “survived” some process. In this example, advisors concentrated incorrectly on the state of the planes that survived, overlooking the planes that didn't.

    This example may not seem like a math problem, but it is. Math is about using reason to not be wrong about things.

    Math is also based on common sense. Can you explain why adding seven stones to five stones is the same as adding five stones to seven stones? It’s so obvious that it's difficult to actually explain.

    Math is the reflection of things we already know intuitively. In this case, math reflects our intuition by defining addition as commutative: for any choice of a and b, a + b = b + a.

    Even though we can't solve entire equations with our intuition, mathematics is derived from our common sense.

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    What is How Not to Be Wrong about?

    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.

    How Not to Be Wrong Review

    How Not to Be Wrong by Jordan Ellenberg (2014) is an engaging exploration of the power of mathematical thinking in everyday life. Here's why this book is definitely not boring:

    • Packed with fascinating examples and anecdotes, it demonstrates how math can be applied to solve real-world problems and make better decisions.
    • The book uncovers the hidden mathematical patterns that shape the world around us, revealing that math is not just for academics but for everyone.
    • Through compelling storytelling and thought-provoking insights, it challenges traditional thinking and encourages readers to approach problems from a mathematical perspective.

    Best quote from How Not to Be Wrong

    Mathematics is the extension of common sense by other means.

    —Jordan Ellenberg
    example alt text

    Who should read 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 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

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    How Not to Be Wrong FAQs 

    What is the main message of How Not to Be Wrong?

    The main message of How Not to Be Wrong is to think critically and avoid common mistakes in reasoning.

    How long does it take to read How Not to Be Wrong?

    The reading time for How Not to Be Wrong varies, but it typically takes several hours. The Blinkist summary can be read in just 15 minutes.

    Is How Not to Be Wrong a good book? Is it worth reading?

    How Not to Be Wrong is worth reading for its valuable insights and practical advice in avoiding common pitfalls.

    Who is the author of How Not to Be Wrong?

    The author of How Not to Be Wrong is Jordan Ellenberg.

    What to read after How Not to Be Wrong?

    If you're wondering what to read next after How Not to Be Wrong, here are some recommendations we suggest:
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    • Algorithms to Live By by Brian Christian & Tom Griffiths
    • The Psychology of Money by Morgan Housel
    • Speed Reading by Kam Knight
    • Atomic Habits by James Clear
    • Tools of Titans by Tim Ferriss