Scientists solve the final part of the Sum of three cubes puzzle

Scientists solve the final part of Sum of Three cubes puzzle
Mathematical puzzles can sometimes take a frustrating amount of time to solve(Credits - Pixabay)

A team of scientists from the University of Bristol and Massachusetts Institute of Technology(MIT) has finally solved the last part of the famed mathematics puzzle of 65 years thus finding the answer for 42, the most elusive number.
The problem was set at the University of Cambridge in 1954. The aim was to find the solutions for the equation x3 + y3 + z3 = k, where k could take any value from one to a hundred. It is a Diophantine Equation in which the number of equations are lesser than the number of variables involved. In a mathematical sense, they define an algebraic surface, algebraic curve. The equation gets its name from Diophantus of Alexandria, a mathematician who lived in the 3rd century. The mathematical study of such type of problems is called Diophantine analysis.
The problem of sum-of-three-cubes became quite interesting as the smaller solutions were found easily but then the other answers could not be calculated as the numbers satisfying became too large. With progress in time, each value of k was either found out or proved unsolvable with the help of modern computation techniques except for two numbers 33 and 42.
Professor Andrew Booker with his mathematical genius was able to find a solution when k is 33 taking the help of a university supercomputer. This meant that the last remaining number to find a solution for was 42. Solving it was a task of higher complexity hence Professor Booker sought the help of Andrew Sutherland, MIT maths professor who is a world record breaker in parallel computations. To solve it they took the help of Charity Engine, a “global” computer that utilizes unused, idle computational power from more than 500,000 PCs to create a super-green platform that is crowd-sourced and developed from surplus capacity.
It took a million hours to calculate the numbers which are as follows:
X = -80538738812075974, Y = 80435758145817515, Z = 12602123297335631.

This finally completes the famous solutions to the Diophantine Equation covering every single number from 0 to 100. Professor Booker who is based at the School of Mathematics, University of Bristol said that he felt relieved as there was no certainty to have found something. It bears resemblance to predicting earthquakes where there are only rough probabilities to proceed with. In problems like these, the solution might be within days of trying or a hundred years might pass by still there might be no definitive answer.


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