# Kurt Gödel (1906–1978)

## Author of On Formally Undecidable Propositions of Principia Mathematica and Related Systems

## About the Author

Kurt Godel was probably the most outstanding logician of the first half of the twentieth century. Born in Czechoslovakia, Godel studied and taught in Vienna and then came to the United States in 1940 as a member of the Institute for Advanced Study at Princeton University. In 1953 he was made a show more professor at the institute, where he remained until his death in 1978. Godel is especially well known for his studies of the completeness of logic, the incompleteness of number theory, the consistency of the axiom of choice and the continuum hypothesis. Godel is also known for his work on constructivity, the decision problem, and the foundations of computation theory, as well as his views on the philosophy of mathematics; especially his support of a strong form of Platonism in mathematics. (Bowker Author Biography) show less

## Series

## Works by Kurt Gödel

The Annotated Gödel: A Reader's Guide to his Classic Paper on Logic and Incompleteness — Author — 7 copies

Collected works 4 copies

Kurt Gödel: The Princeton Lectures on Intuitionism (Sources and Studies in the History of Mathematics and Physical… (2021) 3 copies

Collected works 2 copies

Philosophie I Maximen 0 / Philosophy I Maxims 0: Philosophie I Max 0 (Kurt Gödel: Philosophische Notizbücher /… (2019) 2 copies

Maximen VI / Maxims VI 1 copy

Godel [Opere di] 1 copy

Foundations of mathematics : Symposium papers commemorating the sixtieth birthday of Kurt Gödel 1 copy

Gödel 1 copy

Collected works, vol II 1 copy

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## Common Knowledge

- Canonical name
- Gödel, Kurt
- Legal name
- Gödel, Kurt Friedrich
- Other names
- GÖDEL, Kurt Friedrich

GÖDEL, Kurt - Birthdate
- 1906-04-28
- Date of death
- 1978-01-14
- Gender
- male
- Nationality
- Austria (birth)

Czechoslovakia

Germany

USA - Cause of death
- death certificate stated "malnutrition and inanition caused by personality disturbance"
- Education
- University of Vienna
- Occupations
- mathematician

logician

philosopher - Awards and honors
- Albert Einstein Award (1951)

National Medal of Science (Mathematics and Computer Science, 1974) - Short biography
- One of the most significant logicians of all time, Gödel's work has had immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.

Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years of age, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.

He also showed that the continuum hypothesis cannot be disproved from the accepted axioms of set theory, if those axioms are consistent. He made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic.

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## Statistics

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- Also by
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- Members
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- Popularity
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- Rating
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However, this really *is* just an annotation of Gödel's paper, with very little added. In particular, there are no proper worked-through examples to provide a context for all the logic proofs, so at the end of the day, unless the reader is already familiar with the subject, he or she is likely to be left wondering, "OK, but so what?".

And one minor nitpick: for reasons that are unstated,

the author has chosen to replace Gödel's original multiplication operator (.) with a centred dot; this leads to places where, for those of us who are from a country that use the same convention as Germany, and a centred dot has quite a different meaning, the text is harder to follow than it should be. I can't imagine why, if he felt the need to change the glyph used for the multiplication operator, he didn't use the ordinary "times" symbol (×) instead, since, as far as I know, that is unambiguous, at least in the relevant context.

… (more)Perhaps I'm being unfair: the author does a great job of rendering the original paper into comprehensible English, including switching Gödel's idiosyncratic naming into something much more accessible to an English speaker. Maybe that was all that he intended to do. But the subtitle if the book is "A Reader's Guide...", and this particular reader was expecting something rather less arcane, bridging the gap between the original paper and a hypothetical non-expert reader who wasn't already familiar with the subject.