We report on the top ten mathematicians with the highest number of articles, citations, and students, based on data from MathSciNet and the Mathematics Genealogy Project

Alfaro, Carlos A

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Journal of Humanistic Mathematics Volume 12 | Issue 1 January 2022 Extremal Mathematicians Carlos A. Alfaro Banco de Mexico Follow this and additional works at: https://scholarship.claremont.edu/jhm  Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Carlos A. Alfaro, "Extremal Mathematicians," Journal of Humanistic Mathematics, Volume 12 Issue 1 (January 2022), pages 238-242. DOI: 10.5642/jhummath.202201.18. Available at: https://scholarship.claremont.edu/jhm/vol12/iss1/18 ©2022 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Extremal MathematiciansCarlos A. Alfaro1Banco de México, Mexico City, 06000 MEXICOcarlos.alfaro@banxico.org.mxSynopsisWe report on the top ten mathematicians with the highest number of articles,citations, and students, based on data from MathSciNet and the MathematicsGenealogy Project.Keywords: mathematical legacy, mathematicians networks, metrics.When I was an undergraduate student, I used to hear that Paul Erdös wasthe most prolific mathematician, that is, the mathematician with more pub-lished papers than any other mathematician alive. Recently, my curiosity ledme to explore the existing tools of the Mathematics Genealogy Project [8]and MathSciNet [7] in order to find out the current status. What I found isthat Ravi P. Agarwal, professor of mathematics at Texas A&M University-Kingsville, is now the mathematician with the highest number of publicationson the MathSciNet database. To satisfy my curiosity completely, I then com-puted Tables 1, 2, and 3, where the top ten mathematicians with the highestnumber of published papers, citations, and Ph.D. students, respectively, arelisted.2My approach was based on the tools of the Mathematics Genealogy Projectand MathSciNet, so it is possible that my results differ from those one mightobtain using other tools such as Google Scholar [6] or ResearchGate [9].1 Carlos A. Alfaro has been working at Banco de México for the last seven years.Recently he began teaching classes at Universidad La Salle México.2 Data used in all three tables were collected on January 15th, 2020, and can be foundat https://alfaromontufar.github.io/MathSciNet.csv.Journal of Humanistic Mathematics Volume 12 Number 1 (January 2022)Carlos A. Alfaro 239# Publications # Citations # Students Name1605 15147 1 Ravi P. Agarwal1445 19170 4 Paul Erdös1369 11196 1 Daniel J. O’Regan1300 1159 1 Edoardo Ballico1258 10023 3 Hari Mohan Srivastava1247 5318 18 Josip Pecaric1110 3847 7 Silvestru Sever Dragomir1077 8935 10 Saharon Shelah1071 1770 2 Ioannis Konstantinos Argyros966 6145 29 Jaume LlibreTable 1: Top ten most prolific mathematicians (data from 1/15/2020, see Footnote 2).The Mathematics Genealogy Project [8] is an initiative of North DakotaState University and the American Mathematical Society aiming to compilea record of mathematical genealogy, that is, a comprehensive database ofadvisor-advisee relationships among mathematicians with doctoral degrees.Information about the graph encoding this database can be found at https://www.genealogy.math.ndsu.nodak.edu/extrema.php. There, we learnthat in 2016, Cosmin Ionita and Pat Quillen used MATLAB to analyze thisgraph, which, at that time, had 200,037 vertices. In 2018, a contest was held,as part of the Graph Drawing 2018 conference, to draw creatively a subgraphof the Mathematics Genealogy project, which only contained the 2,277 math-ematicians who had received doctoral degrees before the year 1900.3At thattime, there were 222,360 mathematicians on the database. Today, as of Jan-uary 14, 2022, the Project boasts 275,169 records!MathSciNet [7] is an electronic publication of the American MathematicalSociety that is the continuation of the paper-based Mathematical Reviews,which dates back to 1940s. The first public beta version of MathSciNetdatabase went live in 1995. Today MathSciNet is a rich database containingreviews, abstracts, and bibliographic information of the mathematical sci-ences literature [1]. It is important to note that the data in this databaseare constantly updated as new literature appears. In January 2020, as I wascollecting my data, MathSciNet had a record of 982,875 authors, an average3 See the contest project description at http://mozart.diei.unipg.it/gdcontest/contest2018/topics.html and check out [2] for a report on the conference. The projectof the winning team can be consulted on the page https://mathematics-genealogy.de.240 Extremal Mathematicians# Publications # Citations # Students Name380 27128 17 Pierre-Louis Lions480 24017 46 Jacques-Louis Lions230 22984 52 Elias Menachem Stein397 20289 30 Barry Martin Simon299 19896 58 Haim Brezis369 19888 51 Chi-Wang Shu1445 19170 4 Paul Erdös479 18556 123 Roger Meyer Temam255 18076 4 Thomas J. R. Hughes287 16765 57 Stanley Joel OsherTable 2: Top ten mathematicians with the highest number of citations (data from1/15/2020, see Footnote 2).of 6.66 publications per author, and the average of citations 28.52. Today,as of January 14, 2022, there are 1,097,213 authors indexed in the databaseaccording to the front page [7]. See [3, 4, 5] to learn more about this database.These two databases offer us different snapshots of extremal mathematicians,that is, those mathematicians that perform at the extremes with respect tovarious measures and metrics of academic performance. Readers can updatethese snapshots if they desire. My tables here were all based on data fromthe first half of 2020. Today in the first month of 2022, the numbers are ofcourse different, but some basic outlines remain the same. For example, itis easy to see that the folks with the highest number of publications are notthe same as the folks who have the highest number of citations, who in turnare not the same as the folks who have had the most number of doctoralstudents. Only two names, Paul Erdős and Roger Meyer Temam show upin two out of three tables — Erdős in Tables 1-2, and Temam in Tables 2-3— but they seem to be the exceptions. These types of observations raiseinteresting questions about what it means to be a top mathematician.More broadly, we should keep in mind that the contributions and the legacyof a mathematician are dispersed between doing research, teaching, directingtheses, writing articles, disseminating mathematics, and reviewing articles,as well as participating in a wide range of other scholarly activities. It isvery important that each mathematician, especially young students, shouldconstruct their own criteria on the values and impact of mathematical workand think carefully about how they can themselves impact society throughtheir mathematics.Carlos A. Alfaro 241# Publications # Citations # Students Name39 72 151 C.-C. Jay Kuo479 18556 123 Roger Meyer Temam205 1410 108 Pekka Neittaanmäki45 38 107 Andrew Bernard Whinston4 0 105 Shlomo Noach Sawilowsky92 1520 101 Willi Jäger24 13 100 Ronold Wyeth Percival King213 1600 100 Alexander Vasil’evich Mikhalëv69 118 95 Erol Gelenbe2 0 95 Leonard Salomon OrnsteinTable 3: Top ten mathematicians with the highest number of doctoral students (data from1/15/2020, see Footnote 2).Acknowledgments. The author would like to thank the editors for con-structive criticism of the manuscript.References[1] American Mathematical Society, “About MathSciNet”, available athttps://mathscinet.ams.org/mathscinet/help/about.html?version=2, last accessed on January 14, 2022.[2] W. Devanny, P. Kindermann, M. Lóffler, I. Rutter, “Graph drawing con-test report,” pages 609–617 in GD 2018: Graph Drawing and NetworkVisualization – 26th International Symposium, GD 2018, Proceedings,edited by T. Biedl and A. Kerren (Lecture Notes in Computer Science,volume 11282 (2018).[3] E. Dunne, “Looking at the mathematics literature,” Notices of theAmerican Mathematical Society, Volume 66 Number 2 (2019), pages227–230.[4] E. Dunne, “Everything in its right place: An expert guide to search-ing with MathSciNet,” Notices of the American Mathematical Society,Volume 66 Number 8 (2019), pages 1320–1324.[5] E. Dunne, “Everything in its right place: Part II: An expert guide tosearching with MathSciNet,” Notices of the American Mathematical So-ciety, Volume 66 Number 9 (2019), pages 1501–1506.242 Extremal Mathematicians[6] Google Scholar, free web-based search engine for scholarly literature,available at https://scholar.google.com/, last accessed on January14, 2022.[7] MathSciNet, subscription-based electronic research review database,available at http://mathscinet.ams.org/, last accessed on January14, 2022.[8] Mathematics Genealogy Project, Mathematics Genealogy Project, A ser-vice of the NDSU Department of Mathematics, in association with theAmerican Mathematical Society, available at https://www.genealogy.math.ndsu.nodak.edu/index.php, last accessed on January 14, 2022.[9] ResearchGate, commercial social networking site for scientists and re-searchers, available at http://www.researchgate.net, last accessed onJanuary 14, 2022.

Extremal Mathematicians

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