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WHEN IS IT RATIONAL TO BELIEVE A MATHEMATICAL STATEMENT 197
computer memory, but they do control their own mathematical actions—be they constructing
proofs or writing programs. It is this area of direct influence that underlies strict scrutiny by
the mathematical community. Insecurities can be excused inasmuch as they are not the fault
of the practitioners, but rather a particularly mathematical form of bad luck—what the
insurance business calls “an act of God”.
The fundamental difference between the two cases, then, is not about the content of the
statements or the reliability of the arguments brought forth to support them. It is, in the last
instance, about due diligence—the feeling that we have done everything in our power to make
the proof as strong and ‘complete’ as it can be. This could be construed as an undue influence
of the extra-mathematical on our notion of proof, but I don’t think it should be. Rather, I
want to argue, we ought to expand our understanding of what is properly mathematical to
include phenomena such as due diligence—not as a foreign sociological influence on pure
mathematical concepts, but as an integral component of what forms mathematical reality.
Jendrik Stelling
University of Rostock
jendrik.stelling@uni-rostock.de
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