Mathematics Colloquium

Thursday, November 21, 1996, 4:00pm

102 Bradley Hall

Professor Catherine Womack

Dartmouth College

speaks on

Re-Solving the Tension Between Plausible and Demonstrative Reasoning in Mathematics

Abstract.Philosopher and mathematician Georg Polya argued that our reliance on what he calls "demonstrative reasoning" (deductive reasoning) in mathematics requires reliance on "plausible reasoning" (inductive
methods). IN this paper I examine the various tasks that mathematicians are required to do (e.g. finding problems to solve, deciding whether a conjecture might be true, finding a proof of the conjecture, confirming that the proof is correct). I argue that, in addition to using plausible reasoning to discover new mathematical conjectures, mathematicians also use plausible reasoning to *justify* the correctness of their proofs. I then suggest ways of extending the use of plausible reasoning to include inductive methods as equally legitimate as classical deductive proof techniques.

Tea. High tea will be served at 3:30pm in the Lounge.
Emmy's. Certain refreshments will be available at the Emmy's after the talk.
Hostess.Marcia Groszek is the hostess. Anybody who is interested in having dinner with the speaker should contact Marcia at 646-2313.