Kurt Friedrich Gödel (/ˈɡɜːrdəl/ GUR-dəl;[2] German: [kʊʁt ˈɡøːdl̩] ⓘ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher.

Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel profoundly influenced scientific and philosophical thinking in the 20th century (at a time when Bertrand Russell,[3] Alfred North Whitehead,[3] and David Hilbert were using logic and set theory to investigate the foundations of mathematics), building on earlier work by Frege, Richard Dedekind, and Georg Cantor.

For example, his grandfather Joseph Gödel was a famous singer in his time and for some years a member of the Brünner Männergesangverein (Men's Choral Union of Brünn).

[8] 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 Klepetař, like many residents of the predominantly German Sudetenländer, "Gödel considered himself always Austrian and an exile in Czechoslovakia".

Beginning at age four, Gödel suffered from "frequent episodes of poor health", which would continue for his entire life.

[12] Gödel attended the Evangelische Volksschule, a Lutheran school in Brünn from 1912 to 1916, and was enrolled in the Deutsches Staats-Realgymnasium from 1916 to 1924, excelling with honors in all his subjects, particularly in mathematics, languages and religion.

During his teens, Gödel studied Gabelsberger shorthand,[13] and criticisms of Isaac Newton, and the writings of Immanuel Kant.

He read Kant's Metaphysische Anfangsgründe der Naturwissenschaft, and participated in the Vienna Circle with Moritz Schlick, Hans Hahn, and Rudolf Carnap.

"[17] 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 Grundzüge der theoretischen Logik (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?

Kurt Gödel's achievement in modern logic is singular and monumental—indeed it is more than a monument, it is a landmark which will remain visible far in space and time.

In that article, he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g., the Peano axioms or Zermelo–Fraenkel set theory with the axiom of choice), that: These theorems ended a half-century of attempts, beginning with the work of Gottlob Frege and culminating in Principia Mathematica and Hilbert's program, to find a non-relatively consistent axiomatization sufficient for number theory (that was to serve as the foundation for other fields of mathematics).

In 1933 Adolf Hitler came to power in Germany, and over the following years the Nazis rose in influence in Austria, and among Vienna's mathematicians.

In June 1936, Moritz Schlick, whose seminar had aroused Gödel's interest in logic, was assassinated by one of his former students, Johann Nelböck.

[25] He developed paranoid symptoms, including a fear of being poisoned, and spent several months in a sanitarium for nervous diseases.

In 1934, Gödel gave a series of lectures at the Institute for Advanced Study (IAS) in Princeton, New Jersey, titled On undecidable propositions of formal mathematical systems.

This result has had considerable consequences for working mathematicians, as it means they can assume the axiom of choice when proving the Hahn–Banach theorem.

[30] During this trip, Gödel was supposed to be carrying a secret letter from Viennese physicist Hans Thirring to Albert Einstein to alert Franklin D. Roosevelt of the possibility of Hitler making an atom bomb.

Economist Oskar Morgenstern recounts that toward the end of his life Einstein confided that his "own work no longer meant much, that he came to the Institute merely ... to have the privilege of walking home with Gödel".

Using Heft 15 [volume 15] of Gödel's still-unpublished Arbeitshefte [working notebooks], John W. Dawson Jr. conjectures that Gödel discovered a proof for the independence of the axiom of choice from finite type theory, a weakened form of set theory, while in Blue Hill in 1942.

In 1949, he demonstrated the existence of solutions involving closed timelike curves, to Einstein's field equations in general relativity.

In the early 1970s, Gödel circulated among his friends an elaboration of Leibniz's version of Anselm of Canterbury's ontological proof of God's existence.

Following the assassination of his close friend Moritz Schlick,[43] Gödel developed an obsessive fear of being poisoned, and would eat only food prepared by his wife Adele.

Gödel believed in an afterlife, saying, "Of course this supposes that there are many relationships which today's science and received wisdom haven't any inkling of.

"[49] In an unmailed answer to a questionnaire, Gödel described his religion as "baptized Lutheran (but not member of any religious congregation).

It partly explores the ramifications of the fact that Gödel's incompleteness theorem can be applied to any Turing-complete computational system, which may include the human brain.

[57] The Kurt Gödel Society, founded in 1987, is an international organization for the promotion of research in logic, philosophy, and the history of mathematics.

In the 2023 movie Oppenheimer, Gödel, played by James Urbaniak, briefly appears walking with Einstein in the gardens of Princeton.