# 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.