Why do mathematicians re-prove theorems?

Philosophia Mathematica 14 (3):269-286 (2006)
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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DOI 10.1093/philmat/nkl009
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Andrew Arana (2015). On the Depth of Szemerédi's Theorem. Philosophia Mathematica 23 (2):163-176.
B. Skow (2013). Are There Genuine Physical Explanations of Mathematical Phenomena? British Journal for the Philosophy of Science 66 (1):axt038.
Carlo Cellucci (2008). The Nature of Mathematical Explanation. Studies in History and Philosophy of Science 39 (2):202-210.
Carlo Cellucci (2008). The Nature of Mathematical Explanation. Studies in History and Philosophy of Science Part A 39 (2):202-210.

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