Abstract / Synopsis
Mathematical proof lies at the foundations of mathematics, but there are several notions of what mathematical proof is, or might be. In fact, the idea of mathematical proof continues to evolve. In this article, I review the body of literature that argues that there are at least two widely held meanings of proof, and that the standards of proof are negotiated and agreed upon by the members of mathematical communities. The formal view of proof is contrasted with the view of proofs as arguments intended to convince a reader. These views are examined in the context of the various roles of proof. The conceptions of proof held by students, and communities of students, are discussed, as well as the pedagogy of introductory proof-writing classes.
© Todd CadwalladerOlsker
Todd CadwalladerOlsker, "What Do We Mean by Mathematical Proof?," Journal of Humanistic Mathematics, Volume 1 Issue 1 (January 2011), pages 33-60. DOI: 10.5642/jhummath.201101.04. Available at: https://scholarship.claremont.edu/jhm/vol1/iss1/4
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