It is conjectured that n is a sum of 3 cubes if n is a number that is not congruent to 4 or 5 mod 9. The number 33 enters this category, but for 64 years no solutions emerged — that is, whether the equation 33 = x³ + y³ + z³ has an integer solution.
So, mathematicians long wondered whether the number 33 could be expressed as the sum of 3 cubes. The problem was cracked by Andrew Booker, a mathematician at the University of Bristol, he eventually discovered that:
8,866,128,975,287,528³ + (–8,778,405,442,862,239)³ + (–2,736,111,468,807,040)³ = 33
The reason it took so long to find a solution for 33 is that searching for the right numerical trio was computationally impractical until Booker devised his own algorithm.