Mathematicians Have Found a Solution to the Sum of Three Cubes

Andrew Booker (Bristol University, UK) and Andrew Sutherland (Massachusetts Institute of Technology) have found a big solution to a math problem known as the sum of three cubes which asks the question of whether an integer or whole number can be represented as the sum of three cubed numbers.

There were already two known solutions for the number 3, both of which involve small numbers: 1³ + 1³ + 1³ and 4³ + 4³ + (-5)³

But mathematicians have been searching for a third for decades. The solution that Booker and Sutherland found is:

5699368212219623807203 + (-569936821113563493509) 3 + (-472715493453327032) 3 = 3

According to Booker, when a number can be expressed as the sum of three cubes, there are infinitely many possible solutions. And they’ve just found the third one!

There’s a reason the third solution for 3 was so hard to find. “If you look at just the solutions for any one number, they look random,” he says. “We think that if you could get your hands on loads and loads of solutions – of course, that’s not possible, just because the numbers get so huge so quickly – but if you could, there’s kind of a general trend to them: that the digit sizes are growing roughly linearly with the number of solutions you find.”

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