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.

Lasse Andersen

My educational background is a masters degree in philosophy & mathematics and a PhD in applied mathematics and road engineering. My personal interests cover philosophy of IT, philosophy of math, programming, machine learning, road engineering.

Also, I enjoy nature quite a bit. Presently, I work at the Danish Road Directorate with rolling resistance modelling and pavement management as the main focus. Besides doing a lot of programming at work (primarily Python) I also experiment with Erlang in my spare time trying to build peer2peer software.