My favorite mathematical theorem is Fermat's Last Theorem:
If an equation is in the form of
$ a^n + b^n = c^n $
and $ n $ > 2, it does not have no solution in non-zero integers in $ a $, $ b $, and $ c $.
While I have not had any actual chance to use this theorem, it is still very fascinating that a theorem can look so simple yet its proof can remain so elusive for centuries.
