Why do mathematicians re-prove theorems?
Philosophia Mathematica 14 (3):269-286 (2006)
Abstract
From ancient times to the present, the discovery and presentation of new proofs of previously established theorems has been a salient feature of mathematical practice. Why? What purposes are served by such endeavors? And how do mathematicians judge whether two proofs of the same theorem are essentially different? Consideration of such questions illuminates the roles that proofs play in the validation and communication of mathematical knowledge and raises issues that have yet to be resolved by mathematical logicians. The Appendix, in which several proofs of the Fundamental Theorem of Arithmetic are compared, provides a miniature case study.DOI
10.1093/philmat/nkl009
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Citations of this work
Robustness, Reliability, and Overdetermination (1981).William C. Wimsatt - 2012 - In Characterizing the Robustness of Science. pp. 61-78.
Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups.Joshua Habgood-Coote & Fenner Stanley Tanswell - forthcoming - Episteme.
A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices.Yehuda Rav - 2007 - Philosophia Mathematica 15 (3):291-320.
References found in this work
Foundations Without Foundationalism: A Case for Second-Order Logic.Stewart Shapiro - 1991 - Oxford, England: Oxford University Press.
Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century.Paolo Mancosu (ed.) - 1996 - Oxford, England: Oxford University Press.
Ideas and Results in Proof Theory.Dag Prawitz & J. E. Fenstad - 1971 - Journal of Symbolic Logic 40 (2):232-234.