On the Nature and Role of Peer Review in Mathematics

References

• Andersen, L. E. 2017a. Acceptable gaps in mathematical proofs. In preparation.
   Google Scholar
• Andersen, L. E. 2017b. Introduction [available upon request]. PhD diss., Aarhus University, Aarhus, Denmark.
   Google Scholar
• Arbib, M. A. 1990. A Piagetian perspective on mathematical construction. Synthese 84:43–58. doi:10.1007/BF00485006.
   Web of Science ®Google Scholar
• Bornmann, L., and H.-D. Daniel. 2006. Potential sources of bias in research fellowship assessments: Effects of university prestige and field of study on approval and rejection of fellowship applications. Research Evaluation 15:209–19. doi:10.3152/147154406781775850.
   Web of Science ®Google Scholar
• Borwein, J., and D. Bailey. 2003. Mathematics by experiment: Plausible reasoning in the 21st century. Wellesley, MA: AK Peters.
   Google Scholar
• Conrey, J. B. 2003. The Riemann hypothesis. Notices of the AMS 50:341–53.
   Google Scholar
• Davis, P. J. 1972. Fidelity in mathematical discourse: Is one and one really two? The American Mathematical Monthly 79:252–63. doi:10.2307/2316620.
   Web of Science ®Google Scholar
• Devlin, K. 2003. When is a proof? In Devlin’s Angle, a column written for the Mathematical Association of America. https://www.maa.org/external_archive/devlin/devlin_06_03.html ( accessed October 21, 2016).
   Google Scholar
• Epstein, D., and S. Levy. 1995. Experimentation and proof in mathematics. Notices of the AMS 42:670–74.
   Google Scholar
• Frans, J., and L. Kosolosky. 2014. Revisiting the reliability of published mathematical proofs: Where do we go next? Theoria 29:345–60. doi:10.1387/theoria.10758.
   Web of Science ®Google Scholar
• Geist, C., B. Löwe, and B. Van Kerkhove. 2010. Peer review and knowledge by testimony in mathematics. In PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice, eds. B. Löwe, and T. Müller, 155–78. London, UK: College Publications.
   Google Scholar
• Gillespie, G. W., D. E. Chubin, and G. M. Kurzon. 1985. Experience with NIH peer review: Researchers’ cynicism and desire for change. Science, Technology, & Human Values 10:44–54. doi:10.1177/016224398501000306.
   Google Scholar
• Glaser, B. G., and A. L. Strauss. 1967. The discovery of grounded theory: Strategies for qualitative research. New Brunswick, NJ: Aldine Transaction.
   Google Scholar
• Grcar, J. 2013. Errors and corrections in mathematics literature. Notices of the American Mathematical Society 60:418–25. doi:10.1090/noti/201304.
   Google Scholar
• Hargens, L. L., and J. R. Herting. 1990. Neglected considerations in the analysis of agreement among journal referees. Scientometrics 19:91–106. doi:10.1007/BF02130467.
   Web of Science ®Google Scholar
• Inglis, M., and J. P. Mejia-Ramos. 2009. The effect of authority on the persuasiveness of mathematical arguments. Cognition and Instruction 27:25–50. doi:10.1080/07370000802584513.
   Web of Science ®Google Scholar
• Jackson, J. L., M. Srinivasan, J. Rea, K. E. Fletcher, and R. L. Kravitz. 2011. The validity of peer review in a general medicine journal. Plos ONE 6:e22475. doi:10.1371/journal.pone.0022475.
   PubMedGoogle Scholar
• Jauch, L. R., and J. R. Wall. 1989. What they do when they get your manuscript: A survey of Academy of Management reviewer practices. Academy of Management Journal 32:157–73. doi:10.2307/256424.
   Web of Science ®Google Scholar
• Lee, C. 2012. A Kuhnian critique of psychometric research on peer review. Philosophy of Science 79:859–70. doi:10.1086/667841.
   Web of Science ®Google Scholar
• Lee, C., C. Sugimoto, G. Zhang, and B. Cronin. 2013. Bias in peer review. Journal of the American Society for Information Science and Technology 64:2–17. doi:10.1002/asi.22784.
   Web of Science ®Google Scholar
• Lindsey, D. 1988. Assessing precision in the manuscript review process: A little better than a dice roll. Scientometrics 14:75–82. doi:10.1007/BF02020243.
   Web of Science ®Google Scholar
• Longino, H. E. 1989. Feminist critiques of rationality: Critiques of science or philosophy of science? Women’s Studies International Forum 12:261–69. doi:10.1016/S0277-5395(89)80004-4.
   Web of Science ®Google Scholar
• Longino, H. E. 1990. Science as social knowledge: Values and objectivity in scientific inquiry. Princeton, NJ: Princeton University Press.
   Google Scholar
• Marsh, H. W., and S. Ball. 1989. The peer review process used to evaluate manuscripts submitted to academic journals: Interjudgmental reliability. Journal of Experimental Education 57:151–69. doi:10.1080/00220973.1989.10806503.
   Web of Science ®Google Scholar
• Mazur, B. 2014. Is it plausible? The Mathematical Intelligencer 36:24–33. doi:10.1007/s00283-013-9398-0.
   Web of Science ®Google Scholar
• Mejia-Ramos, J. P., and K. Weber. 2014. Why and how mathematicians read proofs: Further evidence from a survey study. Educational Studies in Mathematics 85:161–73. doi:10.1007/s10649-013-9514-2.
   Web of Science ®Google Scholar
• Müller-Hill, E. 2011. Die epistemische Rolle formalisierbarer mathematischer Beweise. PhD diss., University of Bonn, Bonn, Germany.
   Google Scholar
• Newton, D. P. 2010. Quality and peer review of research: An adjudicating role for editors. Accountability in Research 17:130–45. doi:10.1080/08989621003791945.
   PubMed Web of Science ®Google Scholar
• Onitilo, A. A., J. M. Engel, S. A. Salzman-Scott, R. V. Stankowski, and A. R. Suhail. 2013. Reliability of reviewer ratings in the manuscript peer review process: An opportunity for improvement. Accountability in Research 20:270–84. doi:10.1080/08989621.2013.804345.
   PubMed Web of Science ®Google Scholar
• Onitilo, A. A., J. M. Engel, S. A. Salzman-Scott, R. V. Stankowski, and A. R. Suhail. 2014. A core-item reviewer evaluation (CoRE) system for manuscript peer review. Accountability in Research 21:109–21. doi:10.1080/08989621.2014.847664.
   PubMed Web of Science ®Google Scholar
• Peters, D. P., and S. J. Ceci. 1982. Peer-review practices of psychological journals: The fate of published articles, submitted again. Behavioral and Brain Sciences 5:187–95. doi:10.1017/S0140525X00011183.
   Web of Science ®Google Scholar
• Pólya, G. 1954. Mathematics and plausible reasoning, volume 1: Induction and analogy in mathematics. Princeton, NJ: Princeton University Press.
   Google Scholar
• Rav, Y. 1999. Why do we prove theorems? Philosophia Mathematica 7:5–41. doi:10.1093/philmat/7.1.5.
   Google Scholar
• Rav, Y. 2007. A critique of a formalist-mechanist version of the justification of arguments in mathematicians’ proof practices. Philosophia Mathematica 15:291–320. doi:10.1093/philmat/nkm023.
   Google Scholar
• Resnik, D. B., and S. A. Elmore. 2016. Ensuring the quality, fairness, and integrity of journal peer review: A possible role of editors. Science and Engineering Ethics 22:169–88. doi:10.1007/s11948-015-9625-5.
   PubMed Web of Science ®Google Scholar
• Rothwell, P. M., and C. N. Martyn. 2000. Reproducibility of peer review in clinical neuroscience: Is agreement between reviewers any greater than would be expected by chance alone? Brain 123:1964–69. doi:10.1093/brain/123.9.1964.
   PubMed Web of Science ®Google Scholar
• Sørensen, H. K. 2016. ‘The end of proof’? The integration of different mathematical cultures as experimental mathematics comes of age. In Mathematical cultures: The London meetings 2012–2014, ed. B. Larvor, 139–60. Basel, Switzerland: Birkhäuser.
   Google Scholar
• Weber, K. 2008. How mathematicians determine if an argument is a valid proof. Journal for Research in Mathematics Education 39:431–59.
   Web of Science ®Google Scholar
• Wood, F. Q. 1997. The peer review process. Canberra, Australia: Government Printing Service, Australian Research Council.
   Google Scholar