What Do We Mean by Mathematical Proof

By Todd D. Cadwalladerolsker. 2011

68 citations recorded by the source corpus.

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

Subfields: Education, Theoretical Computer Science, Philosophy

View Paper: https://www.semanticscholar.org/paper/255accb040e69abd8296d061b975b8c5b5a363e3

Citations in the corpus

• How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, unknown): “…among either philosophers (e.g., Rav, 2007) or mathematics educators (e.g., CadwalladerOlsker, 2011), although we believe that the majority of mathematics educators believe any characterization of proof should be based on the proofs that mathematicians actually produce (CadwalladerOlsker, 2011).”