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Technologos comments on When does an insight count as evidence? - Less Wrong
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Isn't this true of anything and everything in mathematics, at least in principle? If there is "certainly an objective truth or falsehood to P = NP," doesn't that make it falsifiable by your definition?
I know they get overused, but Godel's incompleteness theorems provide important limits to what can and cannot be proven true and false. I don't think they apply to P vs NP, but I just note that not everything is falsifiable, even in principle.