PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
On mathematicians’ different standards when evaluating elementary proofs
Page: 2-67
Many mathematics educators and philosophers of mathematics believe there is an unusually high level of agreement in their evaluations of the validity of a mathematical proof. The data in this paper challenge this assumption. 108 research-active mathematicians were shown an adaptation of a published proof from elementary calculus and were asked to evaluate its validity. 24% of the participants judged the proof to be valid, while 76% indicated the proof was invalid. Applied mathematicians were more likely to judge the proof as valid than the pure mathematicians (43% vs. 17%). Participants who judged the proof to be invalid were more confident in their judgments. These findings suggest that different groups of mathematicians may use different standards in evaluating proofs.