English mathematicians were able to solve a problem that did not succumb to computers and scientists for 64 years: to express the number 33 by the sum of cubes of three numbers.
A question that seems simple goes back to an integer puzzle from at least 1955. It is not excluded that the ancient Greeks in the third century of our era were puzzled over its decision, according to Life Science. The equation is as follows: x^3+y^3+z^3 = k. A number of similar equations were proposed by the mathematician Diophant about 1800 years ago. Their essence is to choose an integer (for example, 8), and then choose the appropriate x, y and z (in this case, it is 2, 1 and -1, respectively).
Mathematicians tried to find as many k values as possible for which this equation is true, and found that for some numbers this is impossible. Thus, they found that any number that, from dividing by 9, gives a residue of 4 or 5, does not have a Diophantine solution.
This applies to 22 numbers less than 100. Of the remaining 78, which must have solutions, scientists have been puzzled for two years: 33 and 42.
Andrew Booker, a professor of mathematics at the University of Bristol, recently dealt with one of them with the help of a computer algorithm created by him. Looking at the numbers, you will understand why the problem could not be solved by a simple search. After a few weeks of calculations, the machine gave the answer: (8 866 128 975 287 528)^3 + (–8 778 405 442 862 239)^3 + (–2 736 111 468 807 040)^3 = 33.
For those who want to figure out exactly how Booker did it, he shot a video where he spoke in detail about the process.
So now there is only one stubborn number less than 100 is 42. Douglas Adams fans and his “Hitchhiker’s Guide to the Galaxy” are certainly not surprised: it took the book supercomputer 7.5 million years to come to this answer to the question about the meaning of life, the Universe and everything else.
The answer to the riddle, which Richard Feynman stumbled upon at one time, was found last year by mathematics from MIT. They described the way in which dry spaghetti can be broken into two parts: one must not only bend them, but twist at a certain angle. And it has nothing to do with sum of cubes.