Over the summer of 2026, thousands of historians of science and mathematics gathered in Edinburgh for a set of summer conferences. The BSHM supported both the workshop “How much: Global histories and material cultures of accountancy and metrology” and panels at the joint ESHS/HSS annual meeting, and the next two blog posts will give you a flavour of these two exciting Edinburgh events!
This July, an early-bird Fringe enthusiast may have been pleasantly surprised when the Edinburgh crowds led them to three particular locations on the western side of the city’s Old Town. Across the Edinburgh International Conference Centre, Edinburgh Futures Institute, and the National Museum of Scotland, the European Society for the History of Science (ESHS) and the History of Science Society (HSS) hosted a five day conference, combining the societies’ annual meetings for the first time. Being an early-stage PhD scholar at my first international conference, I was repeatedly informed of the unusually large scale of this meeting, surpassing that of any preceding history of science conference. And, indeed, it was of a scale unlikely to be met again any time soon. Spanning over 1900 registered attendees and more than 500 organised sessions, it would take several volumes to present any sort of comprehensive insight. Instead, I share here some highlights of the more mathematically themed discussions, spotlighting two of the panels sponsored by the BSHM and sharing my wider takeaways from the week.
Mathematical Instruments in Perspective
The history of mathematics sits at the intersection of histories of conceptual tradition and histories of material tradition. And in no place was this more clearly demonstrated than in the symposium Contested Success and Celebrated Failure: The Practice of Mathematical Instruments in Varied Settings (organised by Michael Korey and Samuel Gessner, sponsored by the BSHM). These sessions were an exemplary reminder of how, when analysing the histories of mathematical instruments, one cannot separate the theoretical underpinnings from their tangible contexts. And when we study instruments as evidence of an intellectual trail, our questions must transform as we uncover new dimensions of the role they played. In fact, Gaye Danisan broke down what it means to study the mathematical-astronomical instruments of the Ottoman Empire into no less than six historical dimensions: their composition, their function, their use, how they were taught, how related knowledge circulated, and how they were adapted and reinterpreted within Ottoman scientific cultures. Moreover, the discovery of unfinished instruments, such as paper Ottoman volvelles (rotating calendric devices, relating phases of the Sun and Moon), proved for Gaye a valuable time capsule into their practical and intellectual context.
Since the third century BCE, the term astrolabe has also been applied broadly to rotational instruments that determine the positions of celestial bodies, used by sailors, surveyors and scholars alike. The resultant dynamics between commerce and scholarship, Giorgio Strano warned us, can create historical pitfalls we must be wary of before making assumptions of either the maker or the scholar. In trying to date pre-Gregorian astrolabes, we learned, one may achieve more accurate results by inspecting the features of the instrument than the date it so shamelessly claims for itself. The Museo Galileo’s overview of the different components that make up an astrolabe reveals just how intricate dating and interpreting these instruments can be.
And these considerations are by no means restricted to cases where the instruments themselves have survived. Davide Crippa and Pietro Milici demonstrated as much through the writings of Giovanni Poleni (1683-1761), exploring how eighteenth-century geometries were used to approach the organic construction of transcendental curves. Whilst the Cartesian geometries proved useful for analysing algebraic curves in the seventeenth century, they were not so immediately suited for problems of a transcendental nature, such as the inverse tangent problem (where one predefines conditions of a curve’s tangent). For example, what curve results when a subtangent is maintained at a constant length? This is the condition defining the tractrix (an illustrative demonstration of this can be explored here). Poleni’s letters not only preserve details of machines designed to trace curves like the tractrix continuously, but emphasise again the multifaceted objectives that the history of a machine often involves. Although its primary purpose was to construct geometrical curves with accuracy, Poleni’s development of the machines must also be understood in light of how their perfection could promote his social standing, scholarly network, and institutional visibility.
This has been a look at only a few of the wonderfully varied instruments represented in this panel, as well as a whistlestop tour of some key factors that must inform how we approach their histories. The strongest impression I was left with, however, was Samuel Gessner and Michael Korey’s invitation to consider that, while a mathematical instrument may itself change over time, its history is also shaped by the changing hands that use it and the changing eyes that judge it.
A Global History of Mathematics
Historians now approach mathematics from a range of perspectives, with focuses on different geographical, conceptual, temporal, and social contexts, to name just a few. When attempting to integrate the resulting range of methodologies into a truly global perspective, one may ask: what reassessment of historiographic norms is needed? And what challenges arise in doing so? Such questions were at the heart of the roundtable Old Problems, New Angles: Toward a Global History of Mathematics (organised by E. A. Hunter and Julia Tomasson, with discussion led by Karine Chemla, sponsored by the BSHM).
Bridging conceptual histories
The challenges of integrating methodologies are especially relevant for historical works that bring together distinct conceptual traditions. Between 813 and 833 CE, the Islamic mathematician al-Khawārizmī wrote an Arabic-language treatise, commonly referred to as al-Jabr, that stood at the intersection of several such traditions, including Greek geometry, Indian and Persian arithmetical practices, and Arabic grammar. In discussion, Marouane ben Miled reflected how a holistic history must acknowledge this intersection while also situating the beginnings of new conceptual traditions, such as algebraic geometry and algebraic arithmetic, and tracing the implications that followed. Particularly compelling was Marouane’s emphasis on the historian’s responsibility to incorporate histories of physical material into any conceptual history, an argument that resonated closely with the themes raised in the Mathematical Instruments session.
Mapping social networks
In discussion, Dhruv Raina turned to the historiography of epistemic violence in colonial India as an example of reapproaching historical dialogues. I appreciated his challenge that, as historians of mathematics increasingly emphasise connectedness in cultures and communities, we must be prepared to open the “black box” of the epistemic hierarchies that come into view. As a practical starting point, Dhruv suggested that the conversation may benefit from looking at the communication networks established during the colonial period, and the form and consequences of the conversations across these networks.
Crossing temporal distances
Temporal distance exists not only between the periods we choose to analyse, but from the past to the present too. To understand the context within which historical figures act, we must carefully avoid imposing modern categorisations upon them. Brigitte Stenhouse emphasised how this was key to her understanding the Scottish mathematician Mary Somerville (1780-1872). Somerville’s pursuit of her passion for mathematics did not take the forms often lauded by modern standards (e.g. publishing papers, producing research results, professorships). As such, the ways in which she wielded her mathematical authority is only interpretable through an understanding of her own individual context. Asking instead what it meant for her to be a mathematician provided Brigitte with a powerful lens for meeting Somerville where she was, and understanding the kind of roles that individuals like Somerville had in unfolding, expanding, and circulating new mathematical knowledge.
The Transmission of Mathematical Knowledge
Mathematical themes were also found dotted across many other panels during the week. One aspect I found particularly striking was how the immense variety of case studies demonstrated not only the channels through which mathematical knowledge can be transmitted, but also the different ways it may be re-purposed across this transmission.
By looking at the pedagogical use of planar instruments, similar to those mentioned above, Chen Ji analysed the way in which astral studies changed as they travelled within the Mathematical Instruments panel. In particular, how the curiosity of a powerful figure – the Kangxi Emperor (1654-1722) – brought Sino-European exchange to the Qing inner palace, when Jesuit priest Ferdinand Verbiest (1623-1688) was employed to instruct him in science and technology. She unpacked how Verbiest modified European prototypes into a uniquely localised form, constructing Simplified Planar Instruments for the teaching of astronomy in the Chinese context, with an influence that ultimately extended beyond the palace. On the other hand, the session Mathematics in Motion: Equations as Mediators for the Circulation of Knowledge (organised by Abigail Taylor-Roth and Sebastian Fernandez-Mulligan) approached knowledge circulation from a more abstract starting point, taking equations and quantification as the focal media for exchange. For example, Abigail explored the path an equation can take across research contexts by looking at how Benoit Mandelbrot (1924-2010) was inspired by Lewis Fry Richardson (1881-1953) to investigate the “coastline paradox” problem. Where Richardson had shown that a coastline’s measured length increases as the measuring scale becomes finer, Mandelbrot reinterpreted this scaling relation through fractional dimension, estimating the west coast of Britain to have a (non-integer!) dimension of approximately 1.25 and using it as a key example in his development of fractal geometry. For both of these cases, the shifts in individual contexts and interests were core to a full appreciation of how the mathematics was reshaped and redistributed. The question of ‘boundaries’ which shape the uptake of particular ideas within certain circles therefore becomes especially pertinent. In the Global Perspectives roundtable, Madeline Muntersbjorn brought to focus her recent research on mathematical literacy, emphasising the epistemic and philological role it could play within a global history of mathematics. Her advocacy for maths literacy initiatives (such as the Algebra Project) led me to ponder the role of mathematical literacy in shaping social boundaries within my own studies of history, where disparities have implicitly affected both the media and directions taken by the mathematical knowledge being transmitted.
This week certainly captured what I enjoy most about the history of science: the extraordinary diversity of subjects and the community of scholars who continue to renew and challenge the field. Having learned about many historical forms of scientific exchange from the conference talks, I was inevitably appreciative of this opportunity for similar exchange with contemporary scholars. One could not help but feel excitement for the history of science’s expansion in new directions, while also having the important opportunity to step back and contemplate its trajectory as a whole. In writing this, I have of course been unable to mention as many of the fantastic contributions as I would have liked. If you would like to explore the full range of works present – both mathematical and beyond – be sure to visit the official conference website.
About the Author
Victoria Zwierzyk-Teles is a PhD student in the history of physics at both the University of Bonn and the University of St Andrews. Her current research looks at the historical evolution of particle and mass-generation concepts in mid-twentieth century quantum field theories.