Samuel Fromm: Gödel’s Incompleteness Theorems

Mathematics today is largely based on Zermelo-Fraenkel set theory with Axiom of Choice (ZFC). However, it turns out that there are statements within ZFC which can neither be proven nor disproven from the axioms of ZFC, assuming that ZFC is consistent (i.e. it does not contain a contradiction). Furthermore, it is impossible to prove that ZFC is consistent within ZFC itself.
Gödel’s incompleteness theorems show that these shortcomings of ZFC are inherent in any “big enough” set of axioms (with some small restrictions). Besides taking a detailed look at the theorems themselves, we will look at their implications and try to give some insight into their proofs.
The talk is directed to a general audience without any previous knowledge in logic.