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On Mathematicians' Different Standards When Evaluating Elementary Proofs
Author(s) -
Inglis Matthew,
MejiaRamos Juan Pablo,
Weber Keith,
Alcock Lara
Publication year - 2013
Publication title -
topics in cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.191
H-Index - 56
eISSN - 1756-8765
pISSN - 1756-8757
DOI - 10.1111/tops.12019
Subject(s) - argument (complex analysis) , mathematical proof , epistemology , calculus (dental) , psychology , mathematics education , mathematics , philosophy , medicine , geometry , dentistry
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.