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Checking correctness in mathematical peer review
1The Hong Kong Polytechnic University, Hong Kong, China.
Social Studies of Science
|September 30, 2023
Summary
Mathematical peer review, while not guaranteeing correctness, is valued by mathematicians for adding certainty to proofs. Acceptance of results also depends on community consensus and time, not just initial publication.
Area of Science:
- Mathematics
- Scholarly Communication
Background:
- Mathematics relies on deductive proof, unlike empirical natural sciences.
- Despite the ideal of replicability, mathematical literature contains errors.
- Verifying mathematical proofs is complex and challenging.
Purpose of the Study:
- To investigate the role and perception of peer review in mathematics.
- To understand how mathematicians assess the correctness and certainty of published results.
Main Methods:
- Analysis of 95 qualitative interviews with mathematics journal editors.
- Examination of over 100 referee reports and peer review correspondence.
Main Results:
- Mathematicians acknowledge peer review doesn't guarantee correctness but still value it for increased certainty.
- Disagreements arise during peer review regarding proof validity and significance.
- Community acceptance and time are crucial for validating mathematical results, beyond initial peer review.
Conclusions:
- Peer review in mathematics provides a valuable layer of scrutiny, enhancing confidence in results.
- The mathematical community plays a vital role in establishing the validity and acceptance of proofs.
- Publication in peer-reviewed journals is a necessary but insufficient step for full acceptance of mathematical findings.
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