An international team of researchers has come up with an ingenious solution for a math problem, with the help of a supercomputer that was programmed to slog through more than a trillion color combination probabilities. If that isn’t interesting enough, the solution has made the news as the largest math proof ever generated, running over 200 terabytes (TB) in size.
Recently published in the arXiv journal, the research was jointly conducted by Oliver Kullmann of UK-based Swansea University, Marijn Heule from the University of Texas and University of Kentucky’s Victor Marek. First posited in the 1980s by mathematician Ronald Graham, the problem, also known as the boolean Pythagorean Triples problem, has long baffled scientists from across the world.
The problem deals with the Pythagorean formula a2 + b2 = c2, and questions the possibility of assigning a color (either red or blue) to each non-negative integer, such that none of the Pythagorean sets of integers a, b and c are of the same color. Graham went so far as to promise a reward of $100 to whoever managed to solve the problem.
To arrive at the solution, the trio took help of the Cube-and-Conquer paradigm, which is basically a more advanced version of the SAT method for tougher math problems. The technique, according to the researchers, makes use of CDCL solvers as well as specialized look-ahead methods. Using a computer, the team was able to reduce the number of permutations and combinations for the supercomputer to go through to around one trillion (down from 102,300).
Given the complexity of the problem, the 800 processor supercomputer slogged for two straight days, before reaching a solution. As the scientists explain, the solution proves that it is possible to color each of the integers in a different ways, without the sets of integers having the same color. However, it is true only up to 7,824, beyond which the answer becomes no.
Although the solution is indeed a valid one, there are several questions surrounding it. For instance, is it really a acceptable proof if it is valid only up to 7,824? Since the solution too big for humans to actually read, one can’t help but wonder if it really exists.