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Philosophia Mathematica Advance Access originally published online on June 9, 2006
Philosophia Mathematica 2006 14(3):269-286; doi:10.1093/philmat/nkl009
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Philosophia Mathematica (III), Vol. 14 No. 3 © The Author [2006]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Why Do Mathematicians Re-prove Theorems?{dagger}

John W. Dawson, Jr*

* Penn State York 1031 Edgecomb Ave., York, Pennsylvania 17403 U. S. A. jwd7too{at}suscom.net

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.


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Y. Rav
A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices
Philosophia Mathematica, October 1, 2007; 15(3): 291 - 320.
[Abstract] [Full Text] [PDF]


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