View source for Kurt Gödel

{{Infobox person
| name = Kurt Gödel
| born = 28 April 1906
| died = 14 January 1978
| nationality = Austrian-born; later American
| occupation = Logician; mathematician; philosopher
| known_for = Incompleteness theorems; mathematical logic; philosophy of mathematics
| notable_work = Incompleteness theorems; work on set theory and logic
}}


'''Kurt Gödel''' (28 April 1906 – 14 January 1978) was a logician, mathematician, and philosopher whose work addressed the foundations of mathematics and formal systems. He examined the limits of formal proof and the relationship between mathematical truth and provability.

His work combined technical results in logic with philosophical implications for knowledge and certainty.

== Early life and education ==
Gödel was born in Brno, then part of Austria-Hungary. He studied mathematics and philosophy at the University of Vienna and became associated with developments in mathematical logic during the interwar period.

His early work emerged in dialogue with foundational debates in mathematics.

== Incompleteness theorems ==
Gödel is known for proving the incompleteness theorems, which show that any sufficiently expressive and consistent formal system cannot prove all true statements within its own framework. The results also demonstrate that such systems cannot establish their own consistency.

These theorems challenged assumptions about the completeness of formal axiomatic systems.

== Foundations of mathematics ==
Gödel addressed questions concerning the nature of mathematical objects and truth. He defended a form of mathematical realism, holding that mathematical entities exist independently of formal systems.

His philosophical views informed his interpretation of logical results.

== Work on set theory ==
Gödel contributed to set theory, including results on the consistency of the axiom of choice and the generalized continuum hypothesis relative to other axioms. His work explored the relative consistency of mathematical systems.

These results complemented his earlier incompleteness findings.

== Relationship to institutions ==
Gödel held academic positions in Europe and later in the United States, including at the Institute for Advanced Study in Princeton. He published selectively and worked largely independently.

He did not establish a formal school.

== Limits and uncertainty ==
Gödel’s philosophical interpretations of his theorems have been debated. Some critics question the extent to which his results support metaphysical conclusions about mathematical truth.

There is no consensus on how far the implications of incompleteness extend.

== Status ==
Kurt Gödel is regarded as a central figure in twentieth-century logic and the philosophy of mathematics. His work continues to be discussed in mathematics, logic, and philosophy.

== Related topics ==

[[Mathematical logic]]

[[Philosophy of mathematics]]

[[Incompleteness theorems]]

[[Set theory]]

[[Category:Logicians]]
[[Category:Mathematicians]]
[[Category:Austrian philosophers]]
[[Category:American philosophers]]
[[Category:20th-century philosophy]]