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Highly complex proofs and implications of such proofs

Aschbacher, Michael (2005) Highly complex proofs and implications of such proofs. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 363 (1835). pp. 2401-2406. ISSN 1364-503X. doi:10.1098/rsta.2005.1655.

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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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Additional Information:© 2005 The Royal Society. Discussion Meeting Issue ‘The nature of mathematical proof’ organized by A. Bundy, M. Atiyah, A. Macintyre and D. Mackenzie. This work was partially supported by NSF-0203417.
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Subject Keywords:complex; proof; simple group; classification
Issue or Number:1835
Record Number:CaltechAUTHORS:20200916-090615838
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Official Citation:Aschbacher Michael 2005 Highly complex proofs and implications of such proofs Phil. Trans. R. Soc. A. 363:2401–2406
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105400
Deposited By: George Porter
Deposited On:16 Sep 2020 20:59
Last Modified:16 Nov 2021 18:42

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