For 10 points, this is what mathematician that proved many geometric theorems in The Elements.
His proof took a finite list of numbers, multiplied them together, and added one. He then  showed that the resulting number is not a multiple of any of the numbers in the original list. His  algorithm involves starting with two numbers and repeatedly subtracting the smaller from the  greater and replacing the greater number with the difference. The proof showed that there were  infinitely many primes and the algorithm computer the greatest common divisor of two numbers.  For 10 points, this is what mathematician that proved many geometric theorems in The Elements.
His proof took a finite list of numbers, multiplied them together, and added one.
Euclid