I would counter that Gödel's Incompleteness theorem has had the greatest effect on the practice of mathematics by inventing digital computing which has revoltionised mathematics - all as a side effect of Turing and Church's proofs of Gödel's theorem.
Turing's proof of Godel's incompleteness devised the Turing machine as a metaphorical device to demonstrate incompleteness - this then led to the whole of computing.
And for Church's proof of Godel's incompleteness he devised the lambda calculus which founded functional programming, McCarthy's LISP, and the Y-combinator of algebraic recursion.
Turing's proof of Godel's incompleteness devised the Turing machine as a metaphorical device to demonstrate incompleteness - this then led to the whole of computing.
And for Church's proof of Godel's incompleteness he devised the lambda calculus which founded functional programming, McCarthy's LISP, and the Y-combinator of algebraic recursion.