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.

Authorship in top-ranked mathematical and physical journals: Role of gender on self-perceptions and bibliographic evidence

“…160-163;Grcar, 2013;Krantz, 2007Krantz, , p. 1510. Aside from some exceptions, such as extremely prestigious journals like the Annals of Mathematics or particularly difficult research results where additional expertise might be sought, a common practice is to engage a single referee in the peer review process (Andersen, 2017;Krantz, 2007). The London Mathematical Society, which publishes many top-ranked journals in particular in pure mathematics, refers to the referee in singular form in its Author Guidelines, noting that "in mathematics it is common for the Referee to know the Authors personally," thus "fine judgement" is required to handle potential biases (London Mathematical Society Guide to Authors, 2020).…”

“…Although a large body of research on the peer review system has been published in the past decades, so far only one systematic study exists that focuses on the particularities of mathematics, namely that by Geist et al (2010); cf. Andersen (2017) and Auslander (2008).…”

Virtue theory of mathematical practices: an introduction

“…In "The role of testimony in mathematics", Line Edslev Andersen, Hanne Andersen, and Henrik Kragh Sørensen provide an explanation for the common practice amongst mathematicians of basing one's beliefs about the correctness of a proof on the testimony of others. The paper builds on and expands earlier work by the first author (Andersen 2017(Andersen , 2020 which shows that whilst mathematicians regard it as an ideal to check every proof before they rely on it in their own work, this epistemic autonomy is rarely attained. Rather, it is common practice to rely on the testimony of others about the correctness of certain proofs.…”

Reading Mathematical Proofs as Narratives

“…In this way, a proof seems to cue readers to activate their scripts about which methodological moves work when. Andersen (2020) has interviewed mathematicians about their proof reading practices when they act as referees for mathematics journals. Based on the interviews, she similarly suggests that mathematicians read proofs against their experience concerning which approaches work to prove different kinds of results.…”