In response to apparent problems in mathematics, Hilbert urged mathematicians to fix them, and Gödel attempted to prove properties of a language by defining it within itself.

“And a- all these issues led, uh, Hilbert to saying, "Please, mathematicians, there seems to be something wrong here. Can't you fix this?" And so Gödel had this idea of trying to prove properties of his language by defining the language within itself.”