  In this paper, we use G\"{o}del's incompleteness theorem as a case study for
investigating mathematical depth. We take for granted the widespread judgment
by mathematical logicians that G\"{o}del's incompleteness theorem is deep, and
focus on the philosophical question of what its depth consists in. We focus on
the methodological study of the depth of G\"{o}del's incompleteness theorem,
and propose three criteria to account for its depth: influence, fruitfulness,
and unity. Finally, we give some explanations for our account of the depth of
G\"{o}del's incompleteness theorem.
