PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Support for proof as a cluster concept: An empirical investigation into mathematicians’ practice
Page: 1404
In a previous RUME paper, I argued that proof in mathematical practice can profitably be viewed as a cluster concept in mathematical practice. I also outlined several predictions that we would expect to hold if proof were a cluster concept. In this paper, I empirically investigate the viability of some of these predictions. The results of the studies confirmed these predictions. In particular, prototypical proofs satisfy all criteria of the cluster concept and their validity is agreed upon by most mathematicians. Arguments that satisfy only some of the criteria of the cluster concept generate disagreement amongst mathematicians with many believing their validity depends upon context. Finally, mathematicians do not agree on what the essence of proof is.