How does Godel's incompleteness theorem affect the way that mathematicians

How does Godel's incompleteness theorem affect the way that mathematicians

How does Godel's incompleteness theorem affect the way that mathematicians understand and see mathematics as well as the world (if at all)? I'm not even close to a mathematician, but even a slight dose of the idea and theorem were enough to affect me so I suppose that I'm curious.

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