An international team of the researchers has produced a data-heavy proof regarding the Pythagorean triples.
The problem that dates back to 1980s discusses the Pythagoras’ Theorem for a right angled triangle, which states that: a2 + b2 = c2, where c is the hypotenuse, a is the perpendicular and b is the base of the right triangle. This problem is satisfied with a particular set of whole integers.
The Boolean Pythagorean triples problem was put forward by Ronald Graham in the 1980s. The famous mathematician questioned the possibility of assigning either red or blue color to every integer in the set that satisfies the Pythagoras’ theorem such that no set of Pythagorean triples has the same color, i.e. none of the all three integers are either all red or all blue.
Since one integer can be a part of more than one Pythagorean triples, therefore, the problem is quite difficult to solve; e.g. 1,2, 5 and 3,4,5 are both Pythagorean triples with 5 as a common integer. Thus, if 5 is blue in the first set of triples, it will remain blue in the second as well whereby either 4 or 3 will have to be red. Hence, 4 can force the numbers in the line to change colors accordingly and may ultimately result in a monochrome Pythagorean triple somewhere in the set.
Now, advanced computational technology has been employed to prove that the Pythagorean triples cannot be colored so that all the sets have a unique color. The computational method adopted to solve this question applied the brute force technique.
The team was rewarded with a check of $100 from Graham. The solution shows that it is possible to form such solutions where no Pythagorean triples are the same color up to 7824. However, no possible unique combinations exist beyond 7824. It took a whopping 200TB to solve this question.
The analysts have criticized the outcome stating that though the team has cracked the problem, it failed to provide the reason for this particular behavior shown by the number 7825. The result has brought the same old question regarding the computational proofs,
“They may be correct, but are they really mathematics?”