On Mathematicians' Different Standards When Evaluating Elementary Proofs. (11th April 2013)

• Record Type: Journal Article
• Authors: Inglis, Matthew; Mejia‐Ramos, Juan Pablo; Weber, Keith; Alcock, Lara
• Is Part Of: Topics in cognitive science. Volume 5:Number 2(2013:Apr.)
• Page Start: 270
• Page End: 282
• Publication Date: 2013-04-11
• Subjects: Cognitive science -- Periodicals; Cognitive Science -- Periodicals; 153.05
• DOI: 10.1111/tops.12019
• Languages: English
• ISSNs: 1756-8757

Abstract

<abstract abstract-type="main" xml:lang="en" id="tops12019-abs-0001"> <title>Abstract</title> <p>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.</p> </abstract>