ESHS/HSS Annual Meeting

Contested Success and Celebrated Failure: The Practice of Mathematical Instruments in Varied Settings II

Session Submission Type: Organized Session

English Abstract

[NB: The following symposium consisting of two panels has been selected by the British Society for the History of Mathematics to receive financial support – subject to it being accepted by the HSS/ESHS programme committee (e-mail from Brigitte Stenhouse to the proponents from 19 November 2025).]

As Jim Bennett recounted, early-modern mathematical instruments created their own reality—or in the words of Gemma Frisius, they could allow practitioners to ‘… do by the inventions of geometry what is not permitted in the natural world’. Given this flexibility, when did practitioners regard their instruments as having succeeded or failed?

This panel explores how the acceptance of an instrument depended not simply on theoretical soundness, but also on contingencies of use, making, and sometimes even patronage. We explore how different actors defined and assessed instruments, and how their categories reveal mathematical rigor, performance, and fitness as historically shifting notions.

We have brought together presentations that extend the increasingly rich scholarship on instruments as material culture, on the role of tacit knowledge in their operation, and on the circulation of artisanal practices essential to their construction. Through our joint examination of mathematical instruments across diverse settings (Ottoman, European, Chinese, Persian; courtly, Jesuit-missionary, artisanal, and academic) we hope to enrich— and further complicate – the idea of a universal mathematics.

Sub Unit

• Organized Session

Chair

• Stefan Zieme, Humboldt University Berlin

Individual Presentations

• A Step in the Right Direction? Debates over Simplifying Calculations on the Celestial Sphere with the Directorium (ca. 1330) - Nicholas A. Jacobson, University of Chicago

• Theoretical Success, Practical Superfluity: The Trajectory of Mercury’s Epicyclic Center in al-Kāshī’s Equatorium - Hamid Bohloul, Postdoctoral Fellow, ASTRA Research Group, Max Planck Institute for the History of Science (MPIWG), Berlin, Germany

• Intractable? Poleni, Mathematical Instruments, and the Circulation of the Tractrix - Davide Crippa, Institute of Philosophy, Czech Academy of Sciences; Pietro Milici, University of Messina

• Analog Sines and Signs of Analogy – Some Clever Instrumental Ways to Lessen Trigonometric Ardor - Samuel GESSNER, Centro Interuniversitário de História das Ciências e da Tecnologia, University of Lisbon; Michael Korey, Mathematisch-Physikalischer Salon (Staatliche Kunstsammlungen Dresden)

Session Organizers

• Michael Korey, Mathematisch-Physikalischer Salon (Staatliche Kunstsammlungen Dresden)

• Samuel GESSNER, Centro Interuniversitário de História das Ciências e da Tecnologia, University of Lisbon