Pi on Earth, or Mathematics in the Real World |
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| Authors: | Bart Van Kerkhove and Jean Paul Van Bendegem |
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| Institution: | (1) Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Vakgroep Wijsbegeerte, Pleinlaan 2, 1050 Brussel, Belgium |
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| Abstract: | We explore aspects of an experimental approach to mathematical proof, most notably number crunching, or the verification of
subsequent particular cases of universal propositions. Since the rise of the computer age, this technique has indeed conquered
practice, although it implies the abandonment of the ideal of absolute certainty. It seems that also in mathematical research,
the qualitative criterion of effectiveness, i.e. to reach one’s goals, gets increasingly balanced against the quantitative
one of efficiency, i.e. to minimize one’s means/ends ratio. Our story will lead to the consideration of some limit cases,
opening up the possibility of proofs of infinite length being surveyed in a finite time. By means of example, this should
show that mathematical practice in vital aspects depends upon what the actual world is like.
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