Search Algorithms Are Changing the Course of Mathematics

Since 1955, mathematicians have used the most powerful computers they can get their hands on to search the number line for trios of integers that satisfy the “sum of three cubes” equation k = x³ + y³ + z³, where k is a whole number. The reason it took so long to find a solution for 33 is that searching far enough up the number line—all the way to 1016, or 10 quadrillion, and just as far down into the negative integers—for the right numerical trio was computationally impractical until Booker devised his algorithm. Previous algorithms “didn’t know what they were looking for,” Booker explained; they could efficiently search a given range of integers for solutions to k = x³ + y³ + z³ for any whole number k, but they weren’t able to target a specific one, like k = 33.

Source: nautil.us