**Gödel** 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.

- Although there is no evidence that he did have a weak heart, Kurt became convinced that he did, and concern for his health became an everyday worry for him.
- Kurt attended school in Brünn, completing his school studies in 1923.
- Gödel entered the University of Vienna in 1923 still without having made a definite decision whether he wanted to specialise in mathematics or theoretical physics.
- The lectures by Furtwängler made the most impact on Gödel and because of them he decided to take mathematics as his main subject.
- This would make a big impact on any student, but on Gödel who was very conscious of his own health, it had a major influence.
- As an undergraduate Gödel took part in a seminar run by Schlick which studied Russell's book Introduction to mathematical philosophy.
- Gödel is best known for his proof of "Gödel's Incompleteness Theorems".
- Another was Hilbert's formalism which was dealt a severe blow by Gödel's results.
- Gödel's results were a landmark in 20th -century mathematics, showing that mathematics is not a finished object, as had been believed.
- Gödel met Zermelo in Bad Elster in 1931.
- The peaceful meeting between Zermelo and Gödel at Bad Elster was not the start of a scientific friendship between two logicians.
- Gödel became a Privatdozent at the University of Vienna in March 1933.
- In 1934 Gödel gave a series of lectures at Princeton entitled On undecidable propositions of formal mathematical systems.
- Despite the health problems, Gödel's research was progressing well and he proved important results on the consistency of the axiom of choice with the other axioms of set theory in 1935.
- However after Schlick, whose seminar had aroused Gödel's interest in logic, was murdered by a National Socialist student in 1936, Gödel was much affected and had another breakdown.
- She was not the first girl that Gödel's parents had objected to, the first he had met around the time he went to university was ten years older than him.
- In March 1938 Austria had became part of Germany but Gödel was not much interested and carried on his life much as normal.
- Most who held the title of privatdozent in Austria became paid lecturers after the country became part of Germany but Gödel did not and his application made on 25 September 1939 was given an unenthusiastic response.
- When the war started Gödel feared that he might be conscripted into the German army.
- In 1940 Gödel arrived in the United States, becoming a U.S. citizen in 1948 (in fact he believed he had found an inconsistency in the United States Constitution, but the judge had more sense than to listen during his interview!).
- One of Gödel's closest friends at Princeton was Einstein.
- It was an injustice which infuriated Gödel; in fact he always took such injustices as personal even although large numbers suffered in the same way.
- After settling in the United States, Gödel again produced work of the greatest importance.
- This did not prove that these axioms were independent of the other axioms of set theory, but when this was finally established by Cohen in 1963 he built on these ideas of Gödel.
- Concerns with his health became increasingly worrying to Gödel as the years went by.
- Adele, Gödel's wife, was a great support to him and she did much to ease the tensions which troubled him.

Born 28 April 1906, Brünn, Austria-Hungary (now Brno, Czech Republic). Died 14 January 1978, Princeton, New Jersey, USA.

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Algebra, Analysis, Group Theory, Origin Czech Republic, Set Theory

Axioms: 1

Branches: 2

Parts: 3 4

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive