John von Neumann:

But von Neumann, who had participated at the Congress, confirmed his fame as an instantaneous thinker, and in less than a month was able to communicate to Godel himself an interesting consequence of his theorem: namely that the usual axiomatic systems are unable to demonstrate their own consistency. However, Godel had already discovered this consequence, now known as his second incompleteness theorem and sent von Neumann a preprint of his article containing both incompleteness theorems. Von Neumann acknowledged Godel's priority in his next letter. He never thought much of "the American system of claiming personal priority for everything."

Please answer a question about this article. If the question is unanswerable, say "unanswerable". What was the consequence of the theory of incompleteness?
usual axiomatic systems are unable to demonstrate their own consistency