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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
Against Mathematical Explanation.Mark Zelcer - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):173-192.
The Nature of Mathematical Explanation.Carlo Cellucci - 2008 - Studies in History and Philosophy of Science Part A 39 (2):202-210.
The Nature of Mathematical Explanation.Carlo Cellucci - 2008 - Studies in History and Philosophy of Science 39 (2):202-210.
Are There Genuine Physical Explanations of Mathematical Phenomena?B. Skow - 2013 - British Journal for the Philosophy of Science 66 (1):axt038.
Proofs of the Compactness Theorem.Alexander Paseau - 2010 - History and Philosophy of Logic 31 (1):73-98.
Similar books and articles
Mathematical Realism and Gödel's Incompleteness Theorems.Richard Tieszen - 1994 - Philosophia Mathematica 2 (3):177-201.
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.
What Do Mathematicians Want? Probabilistic Proofs and the Epistemic Goals of Mathematicians.Don Fallis - 2002 - Logique Et Analyse 45.
On Automating Diagrammatic Proofs of Arithmetic Arguments.Mateja Jamnik, Alan Bundy & Ian Green - 1999 - Journal of Logic, Language and Information 8 (3):297-321.
Added to index2009-01-28
Total downloads97 ( #52,554 of 2,168,604 )
Recent downloads (6 months)2 ( #187,166 of 2,168,604 )
How can I increase my downloads?