The five-yearly joint conference of the British Society for the History of Mathematics and the Canadian Society for the History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, was due to take place in St Andrews in July 2020. Then COVID-19 hit, plunging the world into crisis.
To maintain some solidarity across the History of Mathematics community, and to go a little way towards cheering ourselves up for the postponed conference, the Council of the BSHM decided to hold a smaller-scale, but still international, online meeting. The topically themed ‘Mathematics in Times of Crisis’ meeting on 11 July 2020 was the result. We had a magnificent response to our call for papers, ending up with ten presentations. After some debate we devised a format that proved successful then and has served us well in several subsequent conferences: asking for pre-recorded talks which we grouped together and followed up with live question and answer/discussion sessions with the presenters. Pre-recording took the pressure off presenters who were not yet comfortable with online presentation, but also gave participants in different time zones or with many competing commitments a chance to schedule their own viewing. The live Q&A then gave us an opportunity to interact with the presenters and each other, and lively discussions ensued.
The presentations drew our attention to a wide variety of types of crisis, from internal mathematical crises, like those prompted by Gödel’s incompleteness theorem, or questions of convergence in analysis, through crises of confidence, such as perceptions of British mathematics in the early nineteenth century, or of data processing in the US census, to fully external crises due to war or pestilence. The individuals responding to the crises were equally varied: obscure or famous (or even managing the transition from one to the other), male or female, self-styled mathematicians or not. And the communities of which they were part ranged from artisanal to elite professional mathematicians. The outcomes they devised ranged over new mathematics, reconfigured or translated mathematics, new power dynamics, or innovative mathematical artefacts and processes.
This issue of the BJHM contains expanded versions of three of these presentations and illustrates well the variety of the meeting. Michael Friedman considers the reactions of Hans Hahn and the group around him in Vienna, to the mathematical ‘Crisis of Intuition’ of the 1930s. Rather than considering the resolution of this crisis, Friedman looks at the means by which these mathematicians addressed it. He takes a linguistic approach, looking at how the crisis was referred to and how metaphor was used to describe it, showing that the metaphors relate what at first glace looks like a purely internal mathematical crisis, to crises in external world affairs: the economy, politics, and earthquakes. Stefano Gulizia discusses Kepler’s little-known work on the hexagonal shape of snowflakes, De nive sexangula, placing it at the intersection of mathematical and religious crises. He shows how both these crises motivated the work, but were only two of a complex network of other shaping influences that gave the book its eventual form: courtly etiquette, print culture, and the German workshop tradition. Peggy Kidwell’s paper on ‘Mathematical instruments from times of crisis’ is the most wide-ranging and pulls many of the themes of the meeting together. Kidwell gives voice to a number of otherwise mute artefacts from the Smithsonian Museum, showing how external crises shaped their lives and those of their inventors. Warfare disrupted established supply chains, for example, prompting Simeon de Witt’s invention of a star map, or moved mathematicians to fresh environments, promoting cross-cultural exchanges such as Poncelet’s adoption of the Russian abacus, in addition to more obvious outcomes such as James W Alexander’s invention of a range and deflection corrector for ballistics. The nuclear threat of the Cold War was a different kind of crisis; the ‘Nuclear Bomb Effects Computer’, a circular slide rule, was one grim response. Even in peace time, data overload allied with government need prompted Hermann Hollerith’s invention of a tabulating machine, a forerunner of the programmable computer, and computing allied with renewed warfare provided mathematicians-turned-computer scientists, such as Grace Hopper, with new questions together with disciplinary communities in which to pursue them.
The full meeting programme and abstracts may be found at https://www.bshm.ac.uk/sites/default/files/abstracts_010720.pdf.
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