How Not to Be Wrong: The Power of Mathematical Thinking - by Jordan Ellenberg

How math secretly affects your life

by Bill Gates

The book starts with a story about Abraham Wald, an Eastern European mathematician who worked for the American government during World War II. One day the military came to him and said, “We have a problem. We send our planes overseas, and when they come back, their engines are fine, but their tails are riddled with bullet holes. If we put more armor on the tails, though, the planes get too heavy to fly. Can you help us figure out how to protect the planes’ tails better?”

And he said, “No.”

They were surprised, but then he explained that they were asking the wrong question. “You need to put more armor where there aren’t bullet holes. Clearly, when the plane gets hit in the tail, it makes it back to you. Your problem is the planes that get hit in the engine, because those are the ones that aren’t coming back.”

Ultimately, that’s really what the book is: a series of stories about how a lot of the apparently non-mathematical systems that underpin our daily lives are actually deeply mathematical, and people couldn’t develop them until they started asking the right questions.


What Ellenberg has written is ultimately a love letter to math. If the stories he tells add up to a larger lesson, it’s that “to do mathematics is to be, at once, touched by fire and bound by reason”

How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg

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