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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
Summary
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.
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.
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