Why Mathematicians Re-Prove What They Already Know

The first proof that many people ever learn, early in high school, is the ancient Greek mathematician Euclid’s proof that there are infinitely many prime numbers. It takes just a few lines and uses no concepts more complicated than integers and multiplication. His proof relies on the fact that, if there were a finite number of primes, multiplying them all together and adding 1 would imply the…

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