Image: Stuart Rankin

If you think you had a hard time filling out pages of algebra at school, spare a thought for the three mathematicians who have just published the world’s largest ever proof. It takes up 200TB of storage space.


Nature reports that the team—from the Universities of Texas at Austin, Kentucky and Swansea—made use of bounteous computing resources to solve the Boolean Pythagorean triples problem. What the hell is that, I hear you scream? Seeing as though you’re interested, it asks:

Is it possible to color all the integers either red or blue so that no pythagorean triple of integers a, b, c, satisfying a2+b2=c2 are all the same color?

The puzzle was actually set by mathematician Ronald Graham in the 1980s, and he offered $100 to anyone who could find answer. The trio of researchers have already claimed the reward..


Turns out that the answer to the puzzle is: No. But to reach that simple conclusion, the team had to work through combinations of integers all the way up to 7,825. (The answer was yes up until 7,824.) However, by the time you reach 7,825, it turns out there are more than 102,300 possible ways to color all those integers. The team used some mathematical tricks to simplify the situation, but it still left 1 trillion combinations to check.

The team used the University of Texas’s Stampede supercomputer to churn through all the combinations, utilizing 800 processors over the course of two days to create 200TB of data. (The previous record was a measly 13GB.)

And, of course, that simple answer: No.


These kinds of computer-aided proofs are increasingly common in mathematics, though there is some debate over whether they’re math proofs in the truest sense. Still, most mathematicians can probably agree that the quantity of data required to reach this particular solution was simply to large for any human to every generate.

[arXiv via Nature]