Kurt Gödel

== Early life and education ==

=== Childhood ===
Gödel was born April 28, 1906, in Brünn, [[Austria-Hungary]] (now [[Brno]], [[Czech Republic]]), into the German-speaking family of Rudolf Gödel (1874–1929), the managing director and part owner of a major textile firm, and Marianne Gödel ([[née]] Handschuh, 1879–1966).<ref>Dawson 1997, pp. 3–4.</ref> At the time of his birth the city had a [[German language|German-speaking]] majority which included his parents.<ref>Dawson 1997, p.&nbsp;12</ref> His father was Catholic and his mother was Protestant and the children were raised as Protestants. The ancestors of Kurt Gödel were often active in Brünn's cultural life. For example, his grandfather Joseph Gödel was a famous singer in his time and for some years a member of the {{lang|de|Brünner Männergesangverein}} (Men's Choral Union of Brünn).<ref>Procházka 2008, pp. 30–34.</ref>

Gödel automatically became a citizen of [[Czechoslovakia]] at age 12 when the Austro-Hungarian Empire collapsed following its defeat in the [[First World War]]. According to his classmate {{lang|cs|Klepetař|italic=no}}, like many residents of the predominantly German {{lang|de|[[Sudetenland|Sudetenländer]]}}, "Gödel considered himself always Austrian and an exile in Czechoslovakia".<ref>Dawson 1997, p.&nbsp;15.</ref> In February 1929, he was granted release from his Czechoslovak citizenship and then, in April, granted Austrian citizenship.<ref>{{Cite book|url=https://books.google.com/books?id=5ya4A0w62skC&pg=PA37|title=Collected works|last=Gödel, Kurt|others=Feferman, Solomon|year=1986|isbn=0-19-503964-5|location=Oxford|page=37|oclc=12371326}}</ref> When [[Nazi Germany|Germany]] [[Anschluss|annexed Austria]] in 1938, Gödel automatically became a German citizen at age 32. In 1948, after [[World War II]], at the age of 42, he became an American citizen.<ref>{{cite web |last1=Balaguer |first1=Mark |title=Kurt Godel |url=https://school.eb.com/levels/high/article/Kurt-G%C3%B6del/37162 |website=Britannica School High |publisher=Encyclopædia Britannica, Inc. |access-date=3 June 2019}}</ref>

In his family, the young Gödel was nicknamed {{lang|de|Herr Warum}} ("Mr. Why") because of his insatiable curiosity. According to his brother Rudolf, at the age of six or seven, Kurt suffered from [[rheumatic fever]]; he completely recovered, but for the rest of his life he remained convinced that his heart had suffered permanent damage. Beginning at age four, Gödel suffered from "frequent episodes of poor health", which would continue for his entire life.<ref>{{Cite book |url=http://plato.stanford.edu/archives/win2015/entries/johann-herbart/ |title=Johann Friedrich Herbart |last=Kim |first=Alan |date=2015-01-01 |publisher=Metaphysics Research Lab, Stanford University |editor-last=Zalta |editor-first=Edward N. |edition=Winter 2015 }}</ref>

Gödel attended the {{lang|de|Evangelische Volksschule}}, a Lutheran school in Brünn from 1912 to 1916, and was enrolled in the {{lang|de|Deutsches Staats-Realgymnasium}} from 1916 to 1924, excelling with honors in all his subjects, particularly in mathematics, languages and religion. Although Gödel had first excelled in languages, he later became more interested in history and mathematics. His interest in mathematics increased when in 1920 his older brother Rudolf (born 1902) left for [[Vienna]], where he attended medical school at the [[University of Vienna]]. During his teens, Gödel studied [[Gabelsberger shorthand]],<ref>{{Cite web|url=https://www.helsinki.fi/en/researchgroups/godel-enigma/research/gabelsberger-stenography|title=Gabelsberger stenography &#124; Gödel Enigma &#124; University of Helsinki|website=www.helsinki.fi}}</ref> and criticisms of [[Isaac Newton]], and the writings of [[Immanuel Kant]].<ref>https://academic.oup.com/philmat/article/18/2/166/1525476</ref>

=== Studies in Vienna ===
[[File:GoedelKurt.jpg|thumb|upright=1.4|Plaque to Gödel at 43-45 {{ill|Josefstädter Straße|de}}, [[Vienna]], where he discovered his incompleteness theorems]]
At the age of 18, Gödel joined his brother at the [[University of Vienna]]. He had already mastered university-level mathematics.<ref>Dawson 1997, p.&nbsp;24.</ref> Although initially intending to study [[theoretical physics]], he also attended courses on mathematics and philosophy.<ref>At the University of Vienna, Gödel attended mathematics and philosophy courses side by side with [[Hermann Broch]], who was in his early forties. See: {{cite book|url=https://books.google.com/books?id=BFgpBAAAQBAJ&pg=PA27|title=Kurt Kurt Gödel: Das Album |author=Sigmund, Karl|author-link=Karl Sigmund|author2=Dawson Jr., John W.|author-link2=John W. Dawson Jr.|author3=Mühlberger, Kurt|page=27|publisher=Springer-Verlag|year=2007|isbn=978-3-8348-0173-9}}</ref> During this time, he adopted ideas of [[mathematical realism]]. He read [[Immanuel Kant|Kant]]'s {{lang|de|[[Metaphysical Foundations of Natural Science|Metaphysische Anfangsgründe der Naturwissenschaft]]|italic=yes}}, and participated in the [[Vienna Circle]] with [[Moritz Schlick]], [[Hans Hahn (mathematician)|Hans Hahn]], and [[Rudolf Carnap]]. Gödel then studied [[number theory]], but when he took part in a seminar run by [[Moritz Schlick]] which studied [[Bertrand Russell]]'s book ''Introduction to Mathematical Philosophy'', he became interested in [[mathematical logic]]. According to Gödel, mathematical logic was "a science prior to all others, which contains the ideas and principles underlying all sciences."<ref>Gleick, J. (2011) ''[[The Information: A History, a Theory, a Flood]],'' London, Fourth Estate, p. 181.</ref>

Attending a lecture by [[David Hilbert]] in [[Bologna]] on completeness and consistency in mathematical systems may have set Gödel's life course. In 1928, Hilbert and [[Wilhelm Ackermann]] published {{lang|de|Grundzüge der theoretischen Logik|italic=yes}} (''[[Principles of Mathematical Logic]]''), an introduction to [[first-order logic]] in which the problem of completeness was posed: "Are the axioms of a formal system sufficient to derive every statement that is true in all models of the system?"<ref name="auto">{{Cite conference
 | title = In the Scope of Logic, Methodology and Philosophy of Science
 | volume = 1|conference=11th International Congress of Logic, Methodology and Philosophy of Science, Cracow, August 1999
 | year = 2002|page=291}}
</ref>

This problem became the topic that Gödel chose for his doctoral work.<ref name="auto"/> In 1929, aged 23, he completed his doctoral [[dissertation]] under Hans Hahn's supervision. In it, he established his eponymous [[Gödel's completeness theorem|completeness theorem]] regarding [[first-order logic]].<ref name="auto"/> He was awarded his doctorate in 1930,<ref name="auto"/> and his thesis (accompanied by additional work) was published by the [[Vienna Academy of Science]].