This is a bit of a larger resolution version of
this entry in the Math in movies collection.
It is prompted by the recent discovery
of a solution to the Diophantine equation x^{3} + y^{3} + z^{3}=42 which is
x=-80538738812075974;y=80435758145817515;z=12602123297335631;x^3+y^3+z^3 == 42
found by Andrew Booker from the University of Bristol and Andrew Sutherland.
There are still quite a few such computational challenges ahead. We don't know an answer to
x^{3} + y^{3} + z^{3}=k for
k=114,165,390,579,627,633,732,795,906,921,975 yet.
(Source).
See also This exhibit for Math 21, Fall 2019.
But of course, nothing is as cool as finding the answer to k=42. We just have to find out
what the ultimate question actually is: