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How Not to Be Wrong

The Hidden Maths of Everyday Life

By Jordan Ellenberg
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  • Contains 9 key ideas
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How Not to Be Wrong by Jordan Ellenberg

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.

Key idea 1 of 9

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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