The World's Largest Math Proof Is a Whopping 200 Terabytes in Size

The largest-ever math problem called the Boolean Pythagorean triples problem has been solved by a supercomputer and three computer scientists.
Jessica Miley
The University of Texas’s Stampede supercomputerUniversity of Texas

One of the most elusive maths problems has been solved by three computer scientists and a supercomputer. The proof to Boolean Pythagorean triples problem comes in a 200-terabyte file, making it the world's largest math proof. The size of the file is pretty staggering, 1TB is hard enough to wrap your head around if you are a normal data user let alone 200 of them. The solution has been compressed down into a 68-gigabyte file so that it can be more easily shared among the math community. But those wanting to download the file and have a look and see if they can verify the work will need some pretty serious computing power behind them.

The Boolean Pythagorean triples problem

The 200 terabyte file is now officially the largest-ever computer-assisted proof with the previous record holder being a measly 13 gigabytes. Using supercomputers to assist in creating proofs for combinatorics is pretty common. The 200-terabyte proof solved a combinatorics type of mathematical problem called the Boolean Pythagorean triples. The problem asks whether “each positive integers can be colored either red or blue, so that a combination of three integers a, b, and c, (Pythagorean Triple) can satisfy the Pythagorean equation, a 2 + b 2 =c 2, wherein none of the integers have the same color.” This is an almost impossible task for a single human but when assisted by supercomputers the problem becomes slightly easier.

The World's Largest Math Proof Is a Whopping 200 Terabytes in Size
Source: Marijn Heule

Number theory made the task more manageable

The scientists were able to use number theory to minimize the number of checks of possible combinations the computer had to do. But even with this minimized number, the computer still had to do more than 1 trillion runs. It took two solid days for the Stampede supercomputer to complete this task and produce the 200 terabyte file. Once produced a separate computer was used to verify the proof.

Why 7,824?

Although the computer proved it was possible to color the integers in multiple ways, it did not answer the question why the coloring scheme is possible. And even more baffling, the supercomputer revealed that it was only possible to color the integrals up to 7,824. So in a way, the computer raised even more questions than it answered. Why 7,824? The fact that there is, in the end, no solid 'answers' to the problem has made people question if the whole project is even really math? 

Is using supercomputers really math?

A commonly accepted definition of math is that mathematicians should prioritize human understanding of math rather than gather a growing list of facts. To get all the details and to find out about the whole process you can check out the group's article that is featured in the Cornell University online library.