2134/12150 Matthew Inglis Matthew Inglis Juan P. Mejia-Ramos Juan P. Mejia-Ramos Keith Weber Keith Weber Lara Alcock Lara Alcock On mathematicians' different standards when evaluating elementary proofs Loughborough University 2013 Conviction Proof Evaluation Mathematics Mathematicians 2013-04-19 10:23:37 Journal contribution https://repository.lboro.ac.uk/articles/journal_contribution/On_mathematicians_different_standards_when_evaluating_elementary_proofs/9367433 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.