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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics (BM-PROMA)
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Published on: August 28, 2021

On mathematicians' different standards when evaluating elementary proofs.

Matthew Inglis1, Juan Pablo Mejia-Ramos, Keith Weber

  • 1Mathematics Education Centre, Loughborough University, UK. m.j.inglis@lboro.ac.uk

Topics in Cognitive Science
|April 13, 2013
PubMed
Summary
This summary is machine-generated.

Mathematicians disagreed on calculus proof validity, with applied mathematicians more likely to accept it. This study indicates a lack of a single standard for mathematical proof acceptance.

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Area of Science:

  • Mathematics
  • Mathematical Logic
  • Philosophy of Mathematics

Background:

  • The standard of proof in mathematics is often assumed to be uniform.
  • Previous literature suggests a consensus on proof validity among mathematicians.

Purpose of the Study:

  • To investigate the uniformity of proof validity standards among contemporary mathematicians.
  • To explore factors influencing judgments of proof validity in calculus.

Main Methods:

  • Surveying 109 research-active mathematicians on the validity of a calculus proof.
  • Analyzing disagreements and confidence levels in judgments.
  • Assessing the impact of peer கருத்து on judgments.

Main Results:

  • Substantial disagreement was found regarding the validity of the presented calculus proof.
  • Applied mathematicians were more inclined to accept the proof than pure mathematicians.
  • Those judging the proof invalid were more confident; valid judgments were resistant to change.

Conclusions:

  • Contemporary mathematicians do not exhibit a single, uniform standard for proof validity.
  • Discipline-specific differences (pure vs. applied) influence proof assessment.
  • Cognitive factors like confidence and resistance to persuasion play a role in mathematical judgment.