In the first half of the 20th century the dreams of a complete and consistent formalization of mathematics was destroyed, when Kurt Gödel proved the existence of true but unprovable sentences in every reasonable formalization of mathematics.
However, the explicit sentence constructed in the proof was tailored to cause trouble and therefore was not of much interest to mathematicians in general. Since then various incompleteness phenomena have been discovered and many of these (relative) unprovable sentences are of genuine mathematical interest. In recent years Harvey Friedman have taken this enterprise to a new level by constructing sentences about "low level" mathematics and showed that these sentences are provably equivalent to the consistency of axiomatic systems far stronger than classical set theory (ZFC). In this talk I will try to introduce concepts of mathematical logic together with some highlights in the history of incompleteness phenomena and discuss the philosophical implications of these.
Note that these (early 20th century) developments also play an important role in developing the theoretical computer.
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Schedule for Incompleteness Phenomena in Mathematics: From Kurt Gödel to Harvey Friedman
- Sunday, Aug 28th, 2016, 12:00 (CEST) - Sunday, Aug 28th, 2016, 13:00 (CEST) at Speakers Tent