Last year, MIT scientist Andrew Sutherland helped solve an equation that had vexed the world’s premier mathemeticians for half a century: x³y³z³= k when k=42.
As this MIT news item states, “This sum of three cubes puzzle, first set in 1954 at the University of Cambridge and known as the Diophantine Equation x³y³z³=k, challenged mathematicians to find solutions for numbers 1-100. With smaller numbers, this type of equation is easier to solve: for example, 29 could be written as 3³+ 1³+ 1³, while 32 is unsolvable. All were eventually solved, or proved unsolvable, using various techniques and supercomputers, except for two numbers: 33 and 42.”
A mile or so up the Charles River, the elite ledge scientists of Boston use their own techniques to devise previously unimagined trick algorithms.