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In 2022, Davide Crippa gave three presentations on Bolzano's early research in geometry. The first was given at the conference: "Modern Geometry and its Foundations”, held in Vienna (online), from 13-15 January 2022. The conference was organized by the ERC Starting Grant project "The Roots of Mathematical Structuralism" (PI: Georg Schiemer; Günther Eder) and the FWF project "Purity and Abstraction in Modern Geometry: Historical and Philosophical Perspectives" (PI: Eduardo Giovannini). The second presentation was at a workshop organized by José Ferreiros and M. de Paz in Sevilla (March 07 and 08, 2022). The third talk was given in Utrecht within a conference in history of geometry organized by V. Blasjo and N. Michel in Utrecht. Below you can find the presentation given in Wien, which contains a first overview of Bolzano's "Betrachtungen..."(1804), his seminal work in geometry, as well as some considerations on its philosophical importance and mathematical interest. A conjecture we advanced in the presentation is that Bolzano recognized as a fundamental proposition of (Euclidean) geometry the impossibility of establishing an absolute unit of lenght.
On the occasion of the 26th congress of the International Society of History of Science and Technology held in Prague (online), Davide Crippa and Maria Rosa Massa-Esteve organized a symposium on "Giants and dwarfs in the transformations of mathematics in the XVIII century". The focus of the symposium was on the contributions of “dwarfs”, namely college and/or university teachers, working in countries usually considered at the periphery of scientific research at the time, such as Spain, Bohemia, and Italy. Our idea was to explore how these authors t promoted the circulation and transmission of mathematical knowledge hrough their teaching, especially the kind of mathematics that was considered new during the 18th century, infinitesimal analysis and mixed mathematics. Davide Crippa discussed the trajectory of mixed mathematics in Prague university during the 18th century. His findings are in the presentation below.