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Godel's work abruptly ended a half-century of attempts, beginning with the work of Frege and culminating in Principia Mathematica and Hilbert's formalism, to find a set of axioms sufficient to prove the consistency of all mathematics. The incompleteness theorems also imply that not all mathematical questions are computable.

Godel's work abruptly ended a half-century of attempts, beginning with the work of Frege and culminating in Principia Mathematica and Hilbert's formalism, to find a set of axioms sufficient to prove the consistency of all mathematics. The incompleteness theorems also imply that not all mathematical questions are computable.

This demonstrated the folly of the work of several leaders in the field.  [[Bertrand Russell]] had already published, in Principia Mathematica (1910-13), a massive attempt to axiomatize mathematics.  Gödel's proof also showed that the formalist approach of [[David Hilbert]] was bound to fail to prove consistency.

This demonstrated the folly of the work of several leaders in the field.  [[Bertrand Russell]] had already published, in Principia Mathematica (1910-13), a massive attempt to axiomatize mathematics.  Gödel's proof also showed that the formalist approach of [[David Hilbert]] can not succeed.

Gödel's proof was a landmark for mathematics, demonstrated that it can never be a finished project as many mathematicians had believed.   

Gödel's proof was a landmark for mathematics, demonstrated that it can never be a finished project as many mathematicians had believed.