Mathematicians Solve an Enduring '42' Problem Using massive parallel computing

Sumit Pranav Feb 05, 2020 05:39 AM



Mathematicians have finally figured out the three cubed numbers that sums up to 42. This has solved a problem that has been pondered for more than 65 years. The problem is - can each of the natural numbers below 100 be expressed as the sum of three cubes?


The problem, set in 1954, is exactly what it sounds like: x3+y3+z3=k. K is each of the numbers from 1 to 100; the question is, what are x, y and z?

You can read more about this problem here at wikipedia : https://en.wikipedia.org/wiki/Sums_of_three_cubes

Over the following decades, solutions were found for the easier numbers. In 2000, mathematician Noam Elkies of Harvard University published an algorithm to help find the harder ones. So, we were left with the hardest one of them all: 42.

This proved a much more obstinate problem, so Booker enlisted the aid of fellow MIT mathematician Andrew Sutherland, an expert in massively parallel computation utilized the Charity Engine, an initiative that spans the globe, harnessing unused computing power from over 500,000 home PCs to act as a sort of "planetary supercomputer". It took over a million hours of computing time, but the two mathematicians found their solution.

X = -80538738812075974
Y = 80435758145817515
Z = 12602123297335631

So, the full equation is

(-80538738812075974)3 + 804357581458175153 + 126021232973356313 = 42

Read more details here : https://www.sciencealert.com/mathematicians-solve-a-long-standing-42-problem-using-planetary-supercomputer?perpetual=yes&limitstart=1

 


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Comments


Thirupalu | 05/02/2020 02:47


Wonderful article Sumit.