On the Nature and Role of Peer Review in Mathematics

ABSTRACT

For the past three decades, peer review practices have received much attention in the literature. But although this literature covers many research fields, only one previous systematic study has been devoted to the practice of peer review in mathematics, namely a study by Geist, Löwe, and Van Kerkhove from 2010. This lack of attention may be due to a view that peer review in mathematics is more reliable, and therefore less interesting as an object of study, than peer review in other fields. In fact, Geist, Löwe, and Van Kerkhove argue that peer review in mathematics is relatively reliable. At the same time, peer review in mathematics differs from peer review in most, if not all, other fields in that papers submitted to mathematical journals are usually only reviewed by a single referee. Furthermore, recent empirical studies indicate that the referees do not check the papers line by line. I argue that, in spite of this, mathematical practice in general and refereeing practices in particular are such that the common practice of mathematical journals of using just one referee is justified from the point of view of proof validity assessment. The argument is based on interviews I conducted with seven mathematicians.

KEYWORDS:

• Mathematical journals
• mathematics
• peer review
• proof validation
• refereeing practices
• validation practices

Acknowledgments

This article has benefited much from comments from two referees, Hanne Andersen, Mikkel Willum Johansen, Søren Harnow Klausen, Jan Alexis Nielsen, and Henrik Kragh Sørensen.

Notes

¹ The number of tenured female mathematicians that are Danish and working at Danish universities is very small.

² The number of Danish mathematicians at Danish universities is somewhat small, so, to protect the anonymity of the interviewees, no further information about them will be provided.

³ In Denmark interview studies of this character are exempt from human subject research review (medical studies involving human subjects are, by contrast, required by law to be submitted to such review).

⁴ I thank Mikkel Willum Johansen and Henrik Kragh Sørensen for suggesting this approach.

⁵ I thank a referee for pointing out the importance of considering the role of the editor in quality control in peer review in mathematics.