Math wizards and supercomputers solve ’42’

Two math wizards, after working tirelessly and about 1 million hours of computation, finally found the solution for their problem. Two numbers had proved to be the most difficult to solve in particular. This validated the original question which was, can each of the natural numbers below 100 be expressed as the sum of three cubes.

These numbers were 33 and 42. This, however, was about to change as the solution of the remaining two numbers was finally solved.

To arrive at their solution, however, the duo needed to enlist in Charity Engine, an initiative that spans the globe searching for unused computation power from over 500,000 homes which act as some of ‘planetary supercomputers’. Charity Engine is a free PC app based on Berkeley University’s BOINC software, run by The Worldwide Computer Company Limited.

Andrew Sutherland was an MIT mathematician who had advanced knowledge in massively parallel computations. Andrew Booker saw him as the man he needed in bringing down the curtain of this mathematical problem that had withstood time.

A YouTube Math Channel named Numberphile is what started all this. A mathematician by the name Andrew Booker watched a video that highlighted this very problem about the number 33. This motivated him to create an algorithm he ran using powerful supercomputers and in just three weeks, he had found the solution for the number 33. This meant that only one number was remaining, which was 42. The solution for this number had always proved elusive and difficult to solve and Booker, knowing this, enlisted help from another Mathematician named Andrew Sutherland. The two math wizards went to work.

Math wizards elusive number search

In 1954, a mathematical equation was put forward, which for 65 years remained unsolved. The equation x3+y3+z3=k for numbers ranging from 1 to 100 posed a unique challenge for finding its solution. Basically, K is any number between the ranges of 1 to 100. The problem now was in finding out what numbers x y and z were.

In the decades following this equation, many solutions were found for easy numbers. In the year 2000, with the advancement of computational power, Noam Elkies, a mathematician based in Harvard University came up with a solution that further provided solutions for some unsolved solutions.

Andrew Booker solved the problem of the three cubed numbers by writing an algorithm able to work independently to solve some harder numbers that had stood unsolved up to that year. However, he quickly learned that his algorithm would not solve the entire stack of numbers.

Fast forward to 2019, where the 65-year-old mathematical problem was yet to be solved into its entirety. So how was this solution arrived at?

The solution to the problem ended up being

X = -80538738812075974

Y = 80435758145817515

Z = 12602123297335631

The two Mathematician could not hide their joy and they showed this during their reveal where they changed their personal websites to their solution and named the pages ‘life, the universe, and everything. Booker said:

In this game, it’s impossible to be sure that you’ll find something. It’s a bit like trying to predict earthquakes, in that we have only rough probabilities to go by. So, we might find what we’re looking for with a few months of searching, or it might be that the solution isn’t found for another century.

UK children were reportedly NOT inclined to STEM subjects. In New York, they are thinking of dissolving the Gifted Class due to its discriminatory feature. Elsewhere in the world, children are struggling just to get to school. In all these cases, we can see that children grow up and are nurtured by their current environment, for worst or for the better. How can numbers persist in idle minds?