It was a sensation when Heinrich Scherk discovered in 1834 new minimal
surfaces since during the previous 50 years only the
Catenoid
and the
Helicoid
where known.
(The plane is a minimal surface, but not counted as interesting.)

Two of his discoveries were without singularities, namely
a doubly periodic one which Scherk described as the graph of a function
and a singly periodic one which Scherk presented by an implicit equation.
(doubly periodic = translational symmetries in two directions, singly
periodic = translational symmetries in one direction)

These two surfaces
turned out to be fundamental examples when in the 1980s a wealth of
unexpected minimal surfaces were found. These modern surfaces are all
made with the Weierstrass representation - which leaves Scherk's discoveries
as a singular success, since no methods were found to write down functions
whose graphs are minimal surfaces nor functions which have one minimal
level.