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You may have believed that mathematics at school is a tough nut to crack. You may or may not be pleased to note that it was nothing compared to what three mathematicians have recently come across. While these mathematicians have managed to find a solution to the problem, the only caveat is that it consumes a whopping 200 Terabytes of basic text and requires a supercomputer for processing. Just to put things into perspective, a Terabyte can store 337,920 copies of one of the longest novels called War and Peace.
This complex math problem is actually called the Boolean Pythagorean Triples problem which was initially presented by a mathematician named Ronald Graham in 1980s. As the name may suggest, the problem focuses the Pythagorean formula known to us as as: a2 + b2 = c2.
In the equation, a and b are considered to be a triangle’s shorter sides whereas c is considered as the longest one aka. hypotenuse. One can insert specific sets of three integers called Pythagorean triples in the formula like 32 + 42 = 52, 52 + 122 = 132, and 82 + 152 = 172.
Bearing all that in mind, imagine all integers painted as either blue or red. Ronald Graham raised the question as to whether or not it is possible to paint each integer blue or red such that there is no set that is the same colour. A trio of mathematicians got together to face the challenge as they fed multiple techniques to a Stampede supercomputer in the University of Texas. This helped them narrow down the possible colour combinations to a trillion.
It took the 800-processor strong supercomputer a couple of days to narrow it down further before a solution was arrived at: 7,824. It’s not that simple; though, this solution has forced the trio to create a 68-gigabyte compressed variant of the final figure. That takes nearly 30,000 hours for someone to download and verify. No wonder the team had to employ another supercomputer to take care of that part.
Andrew Moseman from Popular Mechanics went on to state that this is especially tough due to the fact that an integer can be a part of various Pythagorean triples. The same logic can be carried over to big numbers which makes the math problem even more complicated than it is.