We all know that 42 is the answer to life, the universe and everything, thanks to the Hitchhiker's Guide to the Galaxy Now we also know. that this is the sum of three cubes.
For decades, scientists have been asking whether each of the numbers 0 to 100 can be represented as the sum of three cubes, where one cubicle is the same number multiplied three times (two cubes are equal to eight). Forty-two was the last number with no proven solution – so far.
"It's great," MIT mathematician Andrew Sutherland tells Gizmodo. "You're looking and hoping it's there and you just don't know if the algorithm will find it. You wait and wait and just when you are quitting, the number is displayed.
Researchers Andrew Sutherland of MIT and Andrew Booker of the University of Bristol in the United Kingdom found the result using more than a million hours of computing time on the charity engine, according to a press release. Charity Engine is a computer platform that consumes unused processing power of 500,000 home computers to produce a kind of supercomputer worldwide.
The equation, as seen on the home pages of Booker and Sutherland, is:
(- 80538738812075974) ^ 3 + 80435758145817515 ^ 3 + 12602123297335631 ^ 3 = 42
Mathematicians since Louis J. Mordel in the 1950s worked to solve the equation a 3 + b 3 + c 3 = n, where n is the number of interests ( 42 in this case), and a, b and c are the solutions they are looking for. Scientists have found a, b and, c for all numbers less than 100, with the exception of proven exceptions that will have no solution, and 33 and 42.
Most exceptions come from separate proof that all cubes are or multiples of nine or one integer of multiples of nine in the numeric order. This means that three cubes, combined together, can only result in numbers, three or fewer units of multiples of nine – you can never add three cubes to the number of four or five units of multiples of nine. But 33 and 42 were exceptions; both are three units of multiples of nine, but neither has a proven solution. Mathematicians had judged that both numbers (and all numbers except those explicitly forbidden) must have a solution, but there is no proof to say it explicitly.
Motivated by a YouTube video on the subject, Booker created an algorithm to find a solution to these problems and found a solution for n = 33 earlier this year. Now he and Sutherland have found a solution of n = 42 after months of more effort.
"It's like winning the lottery," Sutherland said. "If you play long enough, you will be guaranteed to win, but there is no guarantee of how long it will take."
There are already several numbers less than 1000, with no sum of three cubic solutions, Sutherland explained, but he is more interested in sums of three cubes that produce the number 3. Mathematicians proved that 1 and 2 have infinitely many many predictive model solutions, but found only trivial, easy solutions to 3 (1 cc + 1 cc + 1 cc = 3, for example). They are still wondering when another solution with more numbers will appear.
If this seems like mathematical frivolity, it is not. These Diophantine equations, where you need to understand several unknowns that combine to a certain value, are used when calculating in different algorithms. But what these researchers are actually doing is finding points on elliptic curves is a fundamental mathematical idea used in cryptography that secures things like bitcoin.
But if you are not interested in any of this, just know that the answer to life, the universe and everything now has another properly absurd question to go along with it.