Kurt Gödel and the Foundations of Mathematics

Kurt Gödel (1906-1978)

On April 28, 1906, Kurt Gödel was born. He was one of the most significant logicians of all time. Gödel made an 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 old, 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 (for example 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.

Unfortunately, at yovisto, we don’t have original video footage of Gödel. But we have some lectures from Princeton honoring Kurt Gödel and his works to mark the centenary year of his birth back in 2006:
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