KURT GöDEL
Name: Kurt Godel
Born: 28 April 1906 Brno, Moravia, Austria-Hungary
Died: 14 January 1978 Princeton, New Jersey, U.S.
Kurt Godel (April 28, 1906 Brno (Brunn), Austria-Hungary (now
Czech Republic) - January 14, 1978 Princeton, New Jersey) was an Austrian
American mathematician and philosopher.
One of the most significant logicians of all time, Godel'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
attempting to use logic and set theory to understand the foundations of
mathematics.
Godel 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, Godel
developed a technique now known as Godel 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.
Name: Kurt Godel
Born: 28 April 1906 Brno, Moravia, Austria-Hungary
Died: 14 January 1978 Princeton, New Jersey, U.S.
Kurt Godel (April 28, 1906 Brno (Brunn), Austria-Hungary (now
Czech Republic) - January 14, 1978 Princeton, New Jersey) was an Austrian
American mathematician and philosopher.
One of the most significant logicians of all time, Godel'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
attempting to use logic and set theory to understand the foundations of
mathematics.
Godel 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, Godel
developed a technique now known as Godel 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.