How a scientist solved the mysterious riddle of the number 42

(ORDO NEWS) — For 65 years, mathematicians around the world have been trying to solve a kind of puzzle and find three numbers, the sum of which in the cube would be 42. And, it seems, they finally succeeded.

The problem is as follows: can any number from 1 to 100 be expressed as the sum of three cubes?

If we write down the 1954 formula, we get the following: x 3 + y 3 + z 3 = K.

K in this case is any number from 1 to 100. Accordingly, it was necessary to determine all three unknown variables for each number K in this interval.

In the following decades, solutions were found for prime numbers. In 2000, Harvard University mathematician Noam Elkis published an algorithm that helped find more complex ones. By 2019, only the two most difficult numbers remained unsolved: 33 and 42.

Like many modern discoveries, Youtube contributed to the solution. Mathematician Andrew Booker from the Numberphile channel published a solution to the problem for the number 33, writing his own algorithm.

To do this, he needed a powerful supercomputer at the University’s Advanced Computing Research Center, and he managed to get the solution in just three weeks.

So, we are left with the hardest number: 42. To solve it, Booker enlisted the help of MIT mathematician Andrew Sutherland, an expert in massively parallel computing.

In turn, they turned to the Charity Engine, an initiative that spans the globe, using the residual computing power of more than 500,000 home PCs, resulting in a kind of “planetary supercomputer.”

In total, the calculations took over a million hours, but the answer was still found:

X = -80538738812075974

Y = 80435758145817515

Z = 12602123297335631

So the complete equation looks like this:

(-80538738812075974) 3 + 80435758145817515 3 + 12602123297335631 3 = 42.

“I feel relieved,” Booker said on his blog. And we believe him.


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