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Mathematical method and proof Jeremy Avigad (avigad@cmu.edu)

Summary: Mathematical method and proof
Jeremy Avigad (avigad@cmu.edu)
Carnegie Mellon University
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.
Keywords: Epistemology of mathematics, mathematical proof, automated deduc-
1. Introduction
It is generally acknowledged that at least one goal of mathematics is
to provide correct proofs of true theorems. Traditional approaches to
the philosophy of mathematics have therefore, quite reasonably, tried
to clarify standards of correctness and ground the notion of truth.
But even an informal survey of mathematical practice shows that a


Source: Avigad, Jeremy - Departments of Mathematical Sciences & Philosophy, Carnegie Mellon University


Collections: Multidisciplinary Databases and Resources; Mathematics