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Theory Is Forever pp 15–28Cite as

Mathematical Proofs at a Crossroad?

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3113))

Abstract

For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomatic-deductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental, psychological and social aspects, yesterday only marginal, but now changing radically the very essence of proof. In this paper, we try to organize this evolution, to distinguish its different steps and aspects, and to evaluate its advantages and shortcomings. Axiomatic-deductive proofs are not a posteriori work, a luxury we can marginalize nor are computer-assisted proofs bad mathematics. There is hope for integration!

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Author information

Authors and Affiliations

  1. University of Auckland, New Zealand

    Cristian S. Calude

  2. Romanian Academy, Romania

    Solomon Marcus

Authors
  1. Cristian S. Calude
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  2. Solomon Marcus
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  2. Institute for Information Systems and Computer Media (IICM), Graz University of Technology, A-8010, Graz, Austria

    Hermann Maurer

  3. Institute of Mathematics of the Romanian Academy, PO Box 1-764, 014700, Bucureşti, Romania

    Gheorghe Păun

  4. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

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Calude, C.S., Marcus, S. (2004). Mathematical Proofs at a Crossroad?. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds) Theory Is Forever. Lecture Notes in Computer Science, vol 3113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27812-2_2

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  • DOI: https://doi.org/10.1007/978-3-540-27812-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22393-1

  • Online ISBN: 978-3-540-27812-2

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