Over the following decades, solutions were found for easier numbers. In 2000, mathematician Noam Elkies of Harvard University published an algorithm to help find the harder ones, however, two numbers remained uncracked: 33 and 42.
In 2019, mathematician Andrew Booker from the University of Bristol in the UK saw the problem of three cubes on popular maths channel Numberphile and wrote a new algorithm. He ran the algorithm through a powerful supercomputer at the university's Advanced Computing Research Centre, and got the solution for 33 after just three weeks. So the only number left by the end of 2019 was 42.
The "Life, the Universe, and Everything" number, called so as a nod to Douglas Adams, was researched by Booker and his fellow MIT mathematician Andrew Sutherland, an expert in massively parallel computation. The mathematicians needed the help of a so-called "planetary supercomputer" – the globe-spanning Charity Engine initiative, which harnesses unused computing power from over 500,000 home PCs to do the calculations. Using the algorithm and spending over a million hours of computing time, the two mathematicians found their solution: the cubes of numbers -80538738812075974, 80435758145817515 and 12602123297335631 will create 42 in total.
"I feel relieved," Booker said. "In this game, it's impossible to be sure that you'll find something. It's a bit like trying to predict earthquakes, in that we have only rough probabilities to go by. So, we might find what we're looking for with a few months of searching, or it might be that the solution isn't found for another century."
So with all the numbers 1 to 100 covered, there are plenty of unsolved numbers for 101 to 1000: 114, 165, 390, 579, 627, 633, 732, 906, 921 and 975 still need their solution, so the pair of mathematicians definitely have something to occupy their time and minds in the future.