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Report Montucla Prize 2017

Jemma Lorenat

For her article

Figures real, imagined and missing in Poncelet, and Gergonne
(Issue 42.2, 2015)



In her article, Lorenat analyses five versions of a single conic construction developed between 1817 and 1826 by Poncelet, Plücker and Gergonne. She illustrates their differing methodologies, especially with relation to the status of diagrams in geometry. Lorenat builds upon work by Karine Chemla and others about generality in geometry and work by Dominique Tournès about the notion of “virtual diagram” which he has defined (2012)as a “diagram thatone must have in mind, but that is no longer physically drawn on the paper, or at least which is left to the reader to draw”. The study of the use of such diagrams opens up the question of the relationship between symbols, written speech, and visualization in mathematics. What Lorenat shows is that the failure of written descriptions (such as the reliance upon “imaginary points”) to uniquely produce the intended figure introduces important aspects of generality, a feature often associated with algebra, rather than geometry. Through a painstaking textual analysis, Lorenat provides several examples in which the geometrical practices of Poncelet, Plücker, and Gergonne achieved an indirect mode of imagination, when some geometric forms could not be actually represented. What is especially admirable in this paper is Lorenat’s mature and highly original road into historiographical issues concerning the role of diagrams, generality in mathematics, and mathematical practice that are high on the agenda of historians and philosophers of mathematics. Last but not least, it is a pleasure to read her lucidly written paper.

Also highly commended were (in chronological order of publication):

Alberto Cogliati
Early history of infinite continuous groups, 1883–1898
(Issue 41.3, 2014)

Zhu Yiwen
Different cultures of ;computation ;in seventh century China from the viewpoint of square root extraction
(Issue 43.1, 2016)