Bristol mathematician cracks Diophantine puzzle

A mathematician from the University of Bristol has found a solution to part of a 64-year old mathematical problem - expressing the number 33 as the sum of three cubes. Since the 1950s, mathematicians have wondered if all whole numbers could be expressed as the sum of three cubes; whether the equation k = x³+ y³+ z³ always has a solution. The puzzle is a Diophantine equation in the field of number theory, and forms part of one of the most mysterious and wickedly hard problems in mathematics. We still don't know the answer. As computing power has increased more of these solutions were identified, as well as a group that we know have no solutions; those that leave remainder 4 or 5 when divided by 9. Until recently there were just two more unknown solutions under 100 remaining; 33 and 42. Dr Andrew Booker , Reader of Pure Mathematics from the University's School of Mathematics , has now discovered the solution for number 33: (8,866,128,975,287,528)³ + (-8,778,405,442,862,239)³ + (-2,736,111,468,807,040)³.