It’s a puzzle that’s baffled experts since the 1950s, but now a solution for the Diophantine equation has finally been cracked.
The problem asks if all whole numbers could be expressed as the sum of three cubes - essentially whether k = x³+ y³+ z³ always has a solution.
Until now, mathematicians have struggled to find solutions for just two numbers under 100 - 33 and 42.
Now, Dr Andrew Booker, a mathematician at the University of Bristol, has revealed a solution for one of these numbers.
His solution is: 33 = (8,866,128,975,287,528)³ + (–8,778,405,442,862,239)³ + (–2,736,111,468,807,040)³.
Dr Booker discovered this solution using complex computer search, which took several weeks.
He said: “I had a pretty good guess that I’d find something for one of the numbers below 1000. But I didn’t know it was going to be the number 33.
“We don’t know if the remaining numbers have infinitely many solutions, or how frequent those solutions are. It’s quite mysterious.”
Because the puzzle has been around for so long, many mathematicians believed it was impossible to solve.
Dr Booker added: “This one’s right at the boundary between what we know how to prove and what we suspect might be undecidable.”
The next and final unsolved number under 100 is 42.
