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'''Kurt Gödel''' (1906-1978) was an Austrian mathematician who did pioneering work in logic and the foundations of mathematics. His Incompleteness Theorem demonstrated some limitations of the program that would have placed all of mathematics on an axiomatic basis.
'''Kurt Gödel''' (1906-1978) was an Austrian mathematician who did pioneering work in logic and the foundations of mathematics. His Incompleteness Theorem demonstrated some limitations of the program that would have placed all of mathematics on an axiomatic basis.
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]] can not succeed.
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.
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.