>nature.com
>The puzzle that required the 200-terabyte proof, called the Boolean Pythagorean triples problem, has eluded mathematicians for decades. In the 1980s, Graham offered a prize of US$100 for anyone who could solve it. (He duly presented the check to one of the three computer scientists, Marijn Heule of the University of Texas at Austin, earlier this month.) The problem asks whether it is possible to color each positive integer either red or blue, so that no trio of integers a, b and c that satisfy Pythagoras’ famous equation [math] a^2 + b^2 = c^2 [/math] are all the same color. For example, for the Pythagorean triple 3, 4 and 5, if 3 and 5 were colored blue, 4 would have to be red.
>The numbers 1 to 7,824 can be colored either red or blue so that no trio a, b, and c that satisfy [math] a^2 + b^2 = c^2 [/math] are all the same color. The grid of 7,824 squares here shows one such solution, with numbers colored red or blue (a white square can be either). But for the numbers 1 to 7,825, there is no solution.
>There are more than [math] 10^2300 [/math] ways to color the integers up to 7,825, but the researchers took advantage of symmetries and several techniques from number theory to reduce the total number of possibilities that the computer had to check to just under 1 trillion. It took the team about 2 days running 800 processors in parallel
>arxiv.org
And it only cost them $504,000 in electricity to win that $100.
>CS professors in charged of mathematics
