### Mathematicians Solve Sum-of-Three-Cubes Problem for Number 42

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posted 4:14 pm 10/09/2019 in
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University of Bristol’s Professor Andrew Booker and MIT Professor Andrew Sutherland have found a solution to x3 + y3 + z3 = 42, the famous 65-year-old math puzzle.

The original problem, set in 1954 by University of Cambridge researchers, looked for solutions of the Diophantine equation x3 + y3 + z3 = k, with k being all the numbers from one to 100.

Beyond the easily found small solutions, the problem soon became intractable as the more interesting answers could not possibly be calculated, so vast were the numbers required.

But slowly, over many years, each value of k was eventually solved for (or proved unsolvable), thanks to sophisticated techniques and modern computers — except the last two, the most difficult of all: 33 and 42.

Fast forward to 2019 and Professor Booker’s mathematical ingenuity plus weeks on a supercomputer finally found an answer for 33.

However, solving 42 was another level of complexity.

Professor Booker turned to Professor Sutherland and used the services of Charity Engine, a ‘planetary computer’ that harnesses idle, unused computing power from over 500,000 home PCs to create a crowd-sourced, super-green platform made entirely from otherwise wasted capacity.

The answer, which took over a million hours of calculating to prove, is as follows:

(-80538738812075974)3 + 804357581458175153+ 126021232973356313 = 42

“I feel relieved. In this game it’s impossible to be sure that you’ll find something,” Professor Booker said.

“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.”