Essays on Science and SocietyPORTRAITS OF SCIENCE

Kurt Gödel--Separating Truth from Proof in Mathematics

Science  06 Dec 2002:
Vol. 298, Issue 5600, pp. 1899-1900
DOI: 10.1126/science.1079622

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Summary

Kurt Gödel's Incompleteness Theorem, proved in 1931, showed that it was not possible to formulate a set of axioms that would allow you to prove all of the true facts of mathematics. Gödel's result showed that the axiomatic method, while extremely powerful-it continues to play a central role in mathematics-has inherent limitations. As described in an Essay by Keith Devlin, the Incompleteness Theorem did not lead to any major changes within mathematics, but it changed forever the way mathematicians view the subject.

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