since we cannot know that our interface to the machine is entirely coherent, we may always have to bracket our theories into a residual probability that a bit flipped somewhere in the proof making machine or its verification machine or the interpretation of the verification, etc
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A group of people with mutually accepted and practiced customs, or the customs themselves
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It seems to me that there is an ideal way to do mathematics (I know that this is a crass oversimplification), and the customs of mathematicians are not cultural but pragmatic approximations of this. Deforming them into an idiosyncratic culture perverts mathematics.
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