I want to know the answer to the following question:
What was the central theme of Godel's announcement that the axiomatic system was not complete?
All the background I'm provided with is that "A strongly negative answer arrived in September 1930 at the historic mathematical Congress of Königsberg, in which Kurt Gödel announced his first theorem of incompleteness: the usual axiomatic systems are incomplete, in the sense that they cannot prove every truth which is expressible in their language.". Is that enough to answer the question?