Most times the mathematical problems we are faced with focus on the outcome. For example, what is the sum of 1+1? Or what is 2 x 328? And today, thanks to smartphones, we have calculators with us at all times. But in 1954, mathematicians proposed a question that would end up requiring about 65 years and a supercomputer to answer.
"Can each of the natural numbers below 100 be expressed as the sum of three cubes?"
Over the course of the next 65 years, most of these numbers would be answered for. With the harder of the numbers being taken care of shortly after the year 2000, thanks to an algorithm developed by mathematician Noam Elkies of Harvard University.
But still, as recent as this year, there were two very difficult numbers remaining: 33 and 42.
Enter a mathematician from the University of Bristol, Andrew Booker. After watching a Youtube video about the problem with 33, he decided to write an algorithm of his own. And after only three weeks, Booker had his answer.
So of course, 42 was next on the list for Booker, seeing as it was the only remaining natural number that had yet to be solved for. And as if the winner of a battle royal, 42 was standing firm and strong as the most difficult of the numbers. After all, it is the answer to life, the universe, and everything.
Booker soon realized he needed help. He then called upon fellow MIT mathematician Andrew Sutherland, an expert in massively parallel computation, and together they figured out the problem with 42. Albeit, not in three weeks.
The number 42 didn't go down without a fight. Booker and Sutherland had to employ the services of the Charity Engine, a "planetary supercomputer" that combines the computing power of almost half a million PCs from all over the world, and after more than one million hours of computing time, 42 surrendered, and the pair had their answer.
X = -80538738812075974
(read as: negative eighty quadrillion, five-hundred thirty-eight trillion, seven-hundred thirty-eight billion, eight-hundred twelve million, seventy-five thousand, nine-hundred seventy-four)
Y = 80435758145817515
(read as: eighty quadrillion, four-hundred thirty-five trillion, seven-hundred fifty-eight billion, one-hundred forty-five million, eight-hundred seventeen thousand, five-hundred fifteen)
Z = 12602123297335631
(read as: twelve quadrillion, six-hundred two trillion, one-hundred twenty-three billion, two-hundred ninety-seven million, three-hundred thirty-five thousand, six-hundred thirty-one)
The full equation looks like this:
(-80538738812075974)3 + 804357581458175153 + 126021232973356313 = 42.
"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," Booker said, expressing his relief.
This is indeed an amazing feat. A decades-old math problem was finally solved using a super computer. However, that was only numbers between 1 and 100. How long will it take to solve for the remaining natural numbers ranging from 101 to 1000?
In case you want to try for yourself, here are the remaining numbers: 114, 165, 390, 579, 627, 633, 732, 906, 921 and 975.
Good luck.
