Mathematical method and proof

Synthese 153 (1):105 - 159 (2006)
Abstract
  On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect
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    Mark Zelcer (2013). Against Mathematical Explanation. Journal for General Philosophy of Science 44 (1):173-192.
    Audrey Yap (2011). Gauss' Quadratic Reciprocity Theorem and Mathematical Fruitfulness. Studies in History and Philosophy of Science Part A 42 (3):410-415.
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