## 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 language | English (US) |
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Pages (from-to) | 270-282 |

Number of pages | 13 |

Journal | Topics in Cognitive Science |

Volume | 5 |

Issue number | 2 |

DOIs | |

State | Published - 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