Hot on the heels of the pioneering Sum-Of-Three-Cubes Solution for Number 33, a team led by the University of Bristol and MIT has solved the final piece of a famous 65-year-old math puzzle for the most elusive number of all – 42.
The original problem posed in 1954 by the University of Cambridge sought solutions to the Diophantine equation x ^ 3 + y ^ 3 + z ^ 3 = k, with k being all integers from one to 100.
Beyond the easy-to-find small solutions, the problem soon becomes insoluble as more interesting they answers – if they really exist – could not probably be calculated, so large were the numbers needed.
But slowly, for many years, every value of k was ultimately decided (or proved insoluble) thanks to sophisticated techniques and modern computers ̵
Fast forward to 2019 and Professor Andrew Booker's mathematical ingenuity plus weeks at the university supercomputer finally found the answer for 33, which means that the last outstanding issue in this perennial puzzle, the hardest nut for breaking it, was this solid favorite of Douglas Adams fans everywhere.
However, solving 42 was another level of complexity. Professor Booker turned to MIT Professor of Mathematics Andrew Sutherland, a world record holder with massive parallel computations, and – as if by additional cosmic coincidence – provided the services of a planetary computing platform reminiscent of "Deep Thought", the giant machine that powers the 42 machine Hitcher for the galaxy.
Professors Booker and Sutherland's decision for 42 will be found using the Charity Engine; A "global computer" that uses idle, unused computing power from over 500,000 home PCs to create a super-green platform created by a crowd made entirely of otherwise lost capacity. prove it is as follows:
X = -80538738812075974 Y = 80435758145817515 Z = 12602123297335631
And with these almost infinitely incredible numbers, the known solutions of the Diophantine equation (1954) may finally be the most well known
Professor Booker, who is based at the School of Mathematics at the University of Bristol, says: "I feel relieved. In this game it is impossible to be sure that you will find something. It's a bit like trying to predict earthquakes since we only have a rough chance of passing.
"So we can find what we are looking for with a few months of searching, or maybe the solution has not been found for another century. "
Materials provided by University of Bristol . Note: Content may be edited for style and length.