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Highly Complex Proofs and Implications of Such Proofs

Michael Aschbacher
Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Vol. 363, No. 1835, The Nature of Mathematical Proof (Oct. 15, 2005), pp. 2401-2406
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/30039737
Page Count: 6
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Highly Complex Proofs and Implications of Such Proofs
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Abstract

Conventional wisdom says the ideal proof should be short, simple, and elegant. However there are now examples of very long, complicated proofs, and as mathematics continues to mature, more examples are likely to appear. Such proofs raise various issues. For example it is impossible to write out a very long and complicated argument without error, so is such a 'proof' really a proof? What conditions make complex proofs necessary, possible, and of interest? Is the mathematics involved in dealing with information rich problems qualitatively different from more traditional mathematics?

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