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Citation rates in mathematics: a study of variation by subdiscipline

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Abstract

Variation of citation counts by subdisciplines within a particular discipline is known but rarely systematically studied. This paper compares citation counts for award-winning mathematicians is different subdisciplines of mathematics. Mathematicians were selected for study in groups of rough equivalence with respect to peer evaluation, where this evaluation is given by the awarding of major prizes and grants: Guggenheim fellowships, Sloan fellowships, and National Science Foundation CAREER grants. We find a pattern in which mathematicians working in some subdisciplines have fewer citations than others who won the same award, and this pattern is consistent for all awards. So even after adjustment at the discipline level for different overall citation rates for disciplines, citation counts for different subdisciplines do not match peer evaluation. Demographic and hiring data for mathematics provides a context for a discussion of reasons and interpretations.

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Notes

  1. The NRC surveyed faculty members on 21 possible variables. “[Faculty survey responses] were generally in agreement that publications and citations were the most important factors in program quality.” (National Research Council 2010, p. 12.) Citations were third behind publications per faculty and grants for mathematics and applied mathematics. (National Research Council 2010, Appendix F.)

  2. Excluded items include Database Expansion Items, which represent an expansion of the scope of coverage. Database Expansion items have included “journal publications in the areas that might be termed Applied Statistics” and “Computer Science not previously considered to be within the scope of the MR Database.” In addition, “various digitization projects around the world are invited to contribute their bibliographic data,” but are not classified (AMS 2011a).

  3. While Math Ed is included as a discipline, JRC Education and Educational Research journals are not included in MathSciNet. We will not consider the subdisciplines of Math Ed and Other.

  4. Information is from the combined membership list downloaded from www.ams.org/cml on October 25, 2010.

  5. Group Vb is no longer surveyed but, contained management science and operations research.

  6. Omitted are the 1,231 departments classified as Group M or Group B composed of U.S. departments granting at most a baccalaureate or master’s degree.

  7. For example, the two largest groups named above are 13 Wolf prize and 10 Fields medal recipients. The Fields medalists were all 40 years of age or younger when receiving their awards in the last decade (a homogeneous group in length of career but a small group) while the 13 Wolf prize recipients are all seniors and, in fact, included six Fields medalists from 1966 to 1982.

  8. The NSF CAREER grant is used by the AAU (2000). See AAU Membership Policy Attachment 1: List of Awards, Fellowships and Memberships labeled as “Collected by The Center for Measuring University Performance.” The NRC only includes PECASE awards, which, in mathematics, are primarily a small subset of CAREER awards.

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Authors and Affiliations

  1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Lawrence Smolinsky

  2. LSU Libraries, Louisiana State University, Baton Rouge, LA, 70803, USA

    Aaron Lercher

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  1. Lawrence Smolinsky
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  2. Aaron Lercher
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Correspondence to Aaron Lercher.

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Smolinsky, L., Lercher, A. Citation rates in mathematics: a study of variation by subdiscipline. Scientometrics 91, 911–924 (2012). https://doi.org/10.1007/s11192-012-0647-3

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