Kurt Gödel

Austrian-American logician, mathematician, and philosopher of mathematics (1906–1978)

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Lived 1906–1978, aged 72United States

United States

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Wikipedia
97 languages
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Era
1906–1978
Aged 72
Awards
6
recognised works

Summary

Updated 2026-06-21

He proved that mathematics can never fully prove itself — that any formal system strong enough to handle basic arithmetic will always contain true statements it cannot demonstrate. The incompleteness theorems didn't just reshape logic; they redrew the borders of what knowledge can be.

Biography

About

Born into a wealthy German-speaking family in Brno on April 28, 1906, Gödel earned his doctorate at the University of Vienna with a proof of the completeness theorem in 1929. Two years later, in 1931, he published the incompleteness theorems — showing that formal axiomatic systems meeting certain conditions cannot decide the truth of all statements about natural numbers and cannot prove their own consistency. He developed Gödel numbering to encode formal expressions as numbers, a technique that made the proof possible. He also demonstrated that neither the axiom of choice nor the continuum hyp…

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In their own words

Sourced, dated quotes from Kurt Gödel

Kurt Gödel

said29 Nov 1972

But every error is due to extraneous factors (such as emotion and education); reason itself does not err.

— Attributed as a remark of 29th November 1972, in Incompleteness (2005) by Rebecca Goldstein

Kurt Gödel

said1967

The completeness theorem, mathematically, is indeed an almost trivial consequence of Skolem 1923a.

— as quoted, from a 1967 letter to Hao Wang, by Hao Wang in From Mathematics to Philosophy, 1974, p. 8

Kurt Gödel

saidundated

Either mathematics is too big for the human mind, or the human mind is more than a machine.

— As quoted in Topoi : The Categorial Analysis of Logic (1979) by Robert Goldblatt, p. 13

Kurt Gödel

saidundated

I like Islam, it is a consistent idea of religion and open-minded.

— As quoted in A Logical Journey: From Gödel to Philosophy (1996) by Hao Wang, p. 148

Kurt Gödel

saidundated

There are other worlds and rational beings of a different and higher kind. The world in which we live is not the only one in which we shall live or have lived.

— As quoted in A Logical Journey: From Gödel to Philosophy (1996) by Hao Wang, p. 316

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