M
ATHEMATICIAN ANDREW
BOOKER was searching
for topics to present
at his children’s math
club when he stum-
bled across a YouTube
video about the sum-
of-three-cubes puzzle. “It was
a case of serendipity,” the Uni-
versity of Bristol mathematics
professor says. The video—pro-
duced by the popular YouTube
channel Numberphile—led him
to solve a curious equation that
has stumped mathematicians for
decades.
In 1825, mathematician S.
Ryley proved in the magazine
Ladies’ Diary that any fraction
can be represented as the sum of
three cubes of fractions. Mathe-
matician Louis Mordell took the
puzzle a step further in 1953,
when he questioned whether the
same type of solution could be
found for x^3 +y^3 +z^3 = k, a diophan-
tine equation, which involves only
positive and negative integers. He
started with the number 3, and
the hunt was on to find solutions
for all integers between 1 and 100.
In some cases, finding the solu-
tion to x^3 +y^3 +z^3 = k is easy enough.
To reach 53, for example, all that’sA worldwide network
of computers helped
solve one of math’s most
elusive problems.STAFF44 December 2019
After 65 Years,
Supercomputers
Finally Solve
This Unsolvable
Math Problem
// BY DAVID GROSSM A N //12