Series: Penn State Logic Seminar
Date: Tuesday, October 31, 2000
Time: 2:30 - 3:20 PM
Place: 307 Boucke Building
Speaker: John Dawson, Mathematics, York College, Penn State
Title: Why Do We Re-Prove Theorems?
Abstract:
This talk will take as its starting point Yehuda Rav's provocative
recent paper "Why do we prove theorems?" (Philosophia Mathematica 7
(1999), pp. 5-41), which participants are urged to read prior to the
session. I will examine what motivates and justifies the practice of
presenting new proofs of previously established theorems, a practice
that may be adduced as evidence in support of Rav's contention that it
is "proofs rather than theorems that are the bearers of mathematical
knowledge". I will also broach the question, "How do mathematicians
judge whether a proof is conceptually distinct from its predecessors?"
Several examples of alternative proofs of theorems will be considered,
including various proofs of the fundamental theorem of arithmetic.