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Mathematics

The Art of Mathematical Proof by Contradiction

Quick fact

The proof that the square root of 2 is irrational is a celebrated proof by contradiction, first devised by the ancient Greeks, likely around 500 BCE, and it overturned the Pythagorean belief that all numbers are rational.

Why this is interesting

You're about to prove that something is true by first imagining it's false — and that leads to a contradiction, so it must be true. But how can assuming the wrong thing ever lead to the right answer?