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This talk will give a gentle introduction to one of the cornerstone insights of mathematical logic: Gödel's unsettling incompleteness theorem, which states:
# There are statements which we know are true but for which we have proof that they will never have proof.
# There are statements for which we can arbitrarily decide whether they should be true or not.
These results wouldn't be surprising if they referred to statements about the real world. But they refer to purely mathematical statements, which are commonly thought to be genuinely objective. In the talk we'll learn that the naive understanding of logic as taught in schools is not tenable: There is a (well-understood) place for faith in mathematics.
The talk is aimed at people who enjoy mathematical thinking, but absolutely no prerequisites in formal logic are needed.
PS: True statements which are not provable – isn't this a paradox? How do we know that those statements are true if not by a proof? The talk will demystify this apparent paradox!
Questions are very much welcome! Drop by at the Curry Club Assembly (in the main hall where most of the assemblies are located, near Gate 2.3 and the virtual reality booth).
* '''[https://rawgit.com/iblech/mathezirkel-kurs/master/superturingmaschinen/faith-in-mathematics.pdf Slides]'''
* [http://math.andrej.com/2008/02/02/the-hydra-game/ Hercula vs. Hydra]
* [https://en.wikipedia.org/wiki/Busy_beaver The Busy Beaver function]
* [https://www.youtube.com/watch?v=sUqwFbbwHQo Talk about super Turing machines] (in German)
* [https://en.wikipedia.org/wiki/Chaitin%27s_constant Chaitin's constant]
* [https://en.wikipedia.org/wiki/List_of_large_cardinal_properties List of large cardinal axioms]
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