Mathematicians
Kurt Godel
KURT GUR-dl (German Goedel)
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Austrian-American logician whose 1931 incompleteness theorems are among the most significant results in the foundations of mathematics: any consistent formal axiomatic system powerful enough to describe basic arithmetic contains true statements it cannot prove, and such a system cannot prove its own consistency from within itself. The result answered, negatively, the most ambitious form of David Hilbert's program to place all mathematics on one finite, provably consistent foundation. Godel emigrated to the United States in 1940, working at the Institute for Advanced Study in Princeton alongside Einstein, and became increasingly consumed by paranoid fear of being poisoned in his final years, eventually starving himself to death after his wife, who prepared all his food, was hospitalized.
Facts
BirthplaceBrno, Austria-Hungary (present-day Czech Republic) 1 Death PlacePrinceton, New Jersey, United States, of self-starvation 1 Nationality / CultureAustrian, later American citizen (naturalized 1948) 1 Defining ContributionThe incompleteness theorems (1931), showing fundamental limits on what any sufficiently powerful consistent formal system can prove about itself. 1 Notable WorkUeber formal unentscheidbare Saetze der Principia Mathematica und verwandter Systeme I (1931) 1 Cross-Tradition Connections
Associated With
Godel proved in 1940 that the negation of CH cannot be proved from standard ZFC set theory, the first half of the independence result completed by Cohen in 1963 (Cohen has no live entity in this atlas to link to).
The incompleteness theorems set a permanent limit on what proof, as a method, can achieve for its own foundations.
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Proofs Credited
Sources
1. The Stanford Encyclopedia of Philosophy
Center for the Study of Language and Information, Stanford University
MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and StatisticsAssociated With: Logic and Foundations, https://mathshistory.st-andrews.ac.uk/Biographies/Godel/Quote, Associated With: Logic and Foundations, https://mathshistory.st-andrews.ac.uk/Biographies/Godel/
He proved fundamental results about axiomatic systems, showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system.
Continuum Hypothesis (Wikipedia)
Wikimedia FoundationAssociated With: Continuum Hypothesis, Independence from ZFC section, second paragraphQuote, Associated With: Continuum Hypothesis, Independence from ZFC section, second paragraph
Kurt Godel proved in 1940 that the negation of the continuum hypothesis, i.e., the existence of a set with intermediate cardinality, could not be proved in standard set theory.
Wikipedia: Godel's Incompleteness Theorems
Wikimedia FoundationProofs Credited: Godel's Incompleteness Theorems, Lead sectionQuote, Proofs Credited: Godel's Incompleteness Theorems, Lead section
These results, published by Kurt Godel in 1931, are important both in mathematical logic and in philosophy of mathematics.
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