PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Value judgments attached to mathematical proofs
Page: 444
In mathematics, it is a common phenomenon to find several proofs for a single result. This inevitably leads us to believe that proofs are far more than a convincing argument. Indeed, it appears that there is considerable interest in the insight that is gained from the reasoning utilized in a proof. With the existence of several proofs of the same theorem, we are then confronted with a question of value judgment, as it is not necessarily the case that one values all proofs of a given theorem equally. In this theoretical report, I attempt to provide a framework that contributes to the discussion regarding value judgments about proofs by providing a comparative language to systematically talk about judgments one may attach to a proof. I argue that proofs can be valued for reasons such as (1) comprehensibility, (2) explanatory power, (3) originality and surprises, and (4) generalizability.