On mathematicians' different standards when evaluating elementary proofs

Matthew Inglis, Juan Pablo Mejia-Ramos, Keith Weber, Lara Alcock

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

In this article, we report a study in which 109 research-active mathematicians were asked to judge the validity of a purported proof in undergraduate calculus. Significant results from our study were as follows: (a) there was substantial disagreement among mathematicians regarding whether the argument was a valid proof, (b) applied mathematicians were more likely than pure mathematicians to judge the argument valid, (c) participants who judged the argument invalid were more confident in their judgments than those who judged it valid, and (d) participants who judged the argument valid usually did not change their judgment when presented with a reason raised by other mathematicians for why the proof should be judged invalid. These findings suggest that, contrary to some claims in the literature, there is not a single standard of validity among contemporary mathematicians.

Original languageEnglish (US)
Pages (from-to)270-282
Number of pages13
JournalTopics in Cognitive Science
Volume5
Issue number2
DOIs
StatePublished - Apr 2013

All Science Journal Classification (ASJC) codes

  • Experimental and Cognitive Psychology
  • Linguistics and Language
  • Human-Computer Interaction
  • Cognitive Neuroscience
  • Artificial Intelligence

Keywords

  • Conviction
  • Evaluation
  • Mathematicians
  • Mathematics
  • Proof

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