Glen Robert Van Brummelen, PhD

Glen studies the interactions between mathematics and science in premodern cultures. He is especially interested in trigonometric methods in ancient Greek, medieval Islamic, and medieval European astronomy. Recently he has been working as a member of the European Research Council-funded team ALFA (Alfonsine Astronomy), exploring the development of spherical astronomy in medieval and early Renaissance Europe and its links to Greek and Islamic predecessors. His research has recently uncovered the beginning of the modern tangent and arc sine functions, and he is currently exploring the origin of our modern decimal positional numeration in the astronomical tables of the 15^th century.

Awards & Honors

Selected Recognitions:

• Membership, Institute for Advanced Study (Princeton, NJ), 2019-2020
• Bavarian Academy of Sciences fellowship (Ptolemaeus Arabus et Latinus), 2020
• Erskine Fellowship, University of Canterbury (Christchurch, NZ), 2010, 2017, 2019
• 3M National Teaching Fellowship, 2017
• Haimo Award for Distinguished Teaching, Mathematical Association of America, 2016
• Pacific Northwest Mathematical Association of America Distinguished Teaching Award, 2015
• Smithsonian Institution Dibner Library Resident Fellowship, 2014
• Heavenly Mathematics was shortlisted for the Neumann Prize, and chosen Outstanding Title of 2013 by Choice magazine
• Senior fellowship, Dibner Institute for History of Science and Technology, Massachusetts Institute of Technology, 2005-2006

Recent Publications

Selected Publications:

• “Decimal fractional notation and the decimal point in 15th-century Italy”, Historia Mathematica 66 (2024), 1-13.
• “Geometry and its branches”, in Routledge Handbook on the Sciences in Islamicate Societies, eds. Sonja Brentjes, Peter Barker, and Rana Brentjes, Taylor and Francis, 2023, pp. 64-79.
• “Tables transformed: Innovations in tabular theory and methods in medieval Islamic astronomy”, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 23 (2022), 105-148.
• “All in: Fifteenth-century manuscripts devoted to Giovanni Bianchini’s astronomy”, in Alfonsine Astronomy: The Written Record, eds. Richard Kremer, Matthieu Husson, and José Chabás, Turnhout: Brepols, 2022, pp. 381-400.
• With Matthieu Husson and Clemency Montelle, “Tools of the table crackers: Using quantitative methods to analyze historical numerical tables”, in Editing and Analyzing Historical Astronomical Tables, eds. Matthieu Husson, Clemency Montelle and Benno van Dalen, Turnhout: Brepols, 2022, pp. 19-52.
• “The tables of planetary latitudes in Jamshīd al-Kāshī’s Khāqānī Zīj”, in Editing and Analyzing Historical Astronomical Tables, eds. Matthieu Husson, Clemency Montelle and Benno van Dalen, Turnhout: Brepols, 2022, pp. 287-329.
• With James Byrne, “Maurolico, Rheticus, and the birth of the secant function”, Journal for the History of Astronomy 52 (2021), 189-211.
• “Before the end of an error: Giovanni Bianchini’s original flawed treatise on the conversion of stellar coordinates”, Archive for History of Exact Sciences, 75 (2021), 109-124.
• Trigonometry: A Very Short Introduction, Oxford University Press, 2020.
• “The tables of planetary latitudes in Jamshid al-Kashi’s Khaqani Zij”, in Editing and Analyzing Historical Astronomical Tables, eds. Matthieu Husson, Clemency Montelle, and Benno van Dalen, Brepols, 2021, pp. 287-329.
• With Matthieu Husson and Clemency Montelle, “Tools of the table crackers: Using quantitative methods to analyze historical numerical tables”, in Editing and Analyzing Historical Astronomical Tables, eds. Matthieu Husson, Clemency Montelle, and Benno van Dalen, Brepols, 2021, pp. 19-52.
• “The end of an error: Bianchini, Regiomontanus, and the tabulation of stellar coordinates”, Archive for History of Exact Sciences 72 (2018), 547-563.
• “Themed history of mathematics courses for humanities students”, in The Courses of History, eds. Amy Shell-Gellasch and Dick Jardine, Mathematical Association of America, 2017, 205-214.
• “Trigonometry for the heavens”, Physics Today 70 (12) (2017), 70-71.
• “Astronomy” and “Mathematics”, Encyclopedia of Islam and the Muslim World, ed. Richard C. Martin, Macmillan Reference, 2016.
• “The value of history in a mathematics classroom”, MOMA Journal 3 (1) (2015), 36-42.
• “The travels of astronomical tables in medieval Islam”, Suhayl 12 (2014), 11-12.
• With J. L. Berggren, “Al-Kuhi’s tilfojelser til Euklid’s Data: The importance of being known”, AIGIS Supplementum III: Festkrift til Christian Marinus Taisbak – 80 ar, 2014.
• Edited with Nathan Sidoli, From Alexandria, Through Baghdad: Surveys and Studies in the Ancient Greek and Medieval Islamic Mathematical Sciences in Honor of J. L. Berggren, Springer, 2014.
• “A survey of research in the mathematical sciences in medieval Islam from 1996 to 2011”, in From Alexandria, Through Baghdad: Surveys and Studies in the Ancient Greek and Medieval Islamic Mathematical Sciences in Honor of J. L. Berggren, Nathan Sidoli and Glen Van Brummelen, eds. (Springer, 2014), pp. 101-123.
• “Zijes”, “Trigonometry”, “Arithmetic”, in Oxford Encyclopedia of Philosophy, Science and Technology in Islam, Oxford University Press, 2014.
• With Taro Mimura and Yousuf Kerai, “Al-Samaw’al’s curious approach to trigonometry”, Suhayl 11 (2013), 9-31.
• Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, 2013.
• “Seeking the divine on earth: The direction of prayer in Islam”, Math Horizons 21 (1) (2013), 15-17.
• “Hippocrates of Chios, “Menelaus of Alexandria” (co-authored with Daphne Rodznyak), and “Precession”, in Encyclopedia of Ancient History, eds. R. Bagnall et al., Wiley, 2014.
• “In search of vanishing subjects: The astronomical origins of trigonometry”, in Recent Developments on Introducing a Historical Dimension in Mathematics Education, Victor Katz and Constantinos Tzanakis, eds. (Mathematical Association of America, 2011), pp. 261-271.
• With Mehdi Aminrazavi, “Umar Khayyam”, in Stanford Encyclopedia of Philosophy (plato.stanford.edu), 2011.
• “Clear sailing with trigonometry: Navigating the seas in 14^th-century Venice”, in Mathematical Time Capsules, Dick Jardine and Amy Shell-Gellasch, eds. (Mathematical Association of America, 2011), pp. 63-71.
• “Filling in the short blanks: Musings on bringing the historiography of mathematics to the classroom”, BSHM Bulletin 25 (2010), 2-9.
• “Al-Kashi”, “Al-Sijzi”, “Al-Biruni”, “Omar Khayyam”, “al-Khwarizmi”, “Levi ben Gerson”, and “Richard of Wallingford”, Oxford Dictionary of the Middle Ages, Oxford University Press, 2010.
• The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton University Press, 2009.
• “The history of trigonometry to 1550”, Encyclopedia of Life Support Systems, UNESCO, 2009.

Affiliations & Memberships

• Canadian Mathematical Society
• Mathematical Association of America
• Association of Christians in the Mathematical Sciences
• History of Science Society
• Canadian Society for History and Philosophy of Mathematics
• British Society for History of Mathematics
• Society of Teaching and Learning in Higher Education
• Commission for the History of Ancient and Medieval Astronomy
• Commission on the History of Science and Technology in Islamic Societies