Rethinking the dynamics of mathematics
What, if anything at all, does Prague’s Old Town Square has to do with the earliest known example of an everywhere continuous nowhere differentiable function?
Furthermore, are the changes in the Bohemian lands in general related to the changes in the teaching of mathematical disciplines there at the end of the 18th century and during the first half of the 19th century?
And is there any link between all that and the later development in the Bohemian lands of certain branches of maths such as descriptive geometry, of some cities in the Austrian Kaisertum, for example Vienna and Innsbruck, or of research movements within and beyond these borders, as in the case the Lvov-Warsaw and the Weierstrass school?
In particular, we are interested on how and why certain mathematical practices were set as a norm and different or new practices were incorporated or emerged in the late 18th century and during the first half of the 19th century.
To this end, we take Prague and the Bohemian lands, as well as Bernard Bolzano, as case studies.
It intends to evoke both the approach and the purpose of the project, but also the context in which the project is focused, namely the late 18th century and the first half of the 19th century, a period in which German, which was the official language, and Czech, which gradually gained in importance, coexisted in the Bohemian lands.
Mathematical practices are rooted in a particular time and context (read, for example, Ferreirós’ Mathematical Knowledge and the Interplay of Practices).
Maths and mathematicians are not restricted to our modern, academic understanding of them (read, for example, Robson’s and Stedall’s The Oxford Handbook of the History of Mathematics).
The temporality of mathematics does not imply its relativisation without further ado, but rather a special relativity, and in any case it is compatible with the age-old belief in its timelessness (read, for example, Epple’s “Between Timelessness and Historiality: On the Dynamics of the Epistemic Objects of Mathematics”).
It has been edited to depict mathematicians (astronomers, surveyors, engineers, etc.) working within and on the transformation of the city. The motto ‘From manuscripts to the city’ does not indicate a starting point and a destination, but rather accounts for the variety of traces that enable our study of mathematical practices.
Furthermore, it has been modernised in a way that alludes to the integration of digital tools in our research. Examples of these are Transkribus (for training a HTR model and developing an innovative viewer for the Bolzano Digital Archive) and Nodegoat (for data analysis and creating visualisations for the general public).
Our approach requires in-depth study of institutions, starting with the University of Prague and the Polytechnic School in Prague, societies or groups, such as the Royal Bohemian Society of Sciences, and individuals, ranging from students and private teachers to university professors and mathematicians, all of whom were involved in the transmission of mathematical practices.
But it also demands studying other actors who were crucial or contributed to the normalisation, incorporation or integration and emergence of mathematical practices, such as imperial authorities, the church, nobles and aristocrats, just as paying attention to other testimonies.
To conduct our research, we combine various disciplines and tools.
Our research relies on a number of printed and handwritten texts from the 18th and 19th centuries. These include published works and drafts, but also notebooks, diaries, examinations, letters, etc. of maths teachers, students and practitioners.
In addition, however, we also study other materials that account for the contexts, e.g. decrees, maps, sermons, or library and book-fair catalogues.
Most of these sources come from archives in the Czech Republic and abroad, mainly in Austria and Germany, although in the case of Bolzano they come primarily from the Bernard Bolzano Collection and the Bolzano Digital Archive that we are building.
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The website was conceived and sketched out by Elías, who is behind the content and editing of most of the images, and was beautifully developed by Mimatik, with both working on the final details. The outcome is the fruit of this to be long-lasting partnership.
PragMatika’s logo was designed by Markéta Jelenová, a Czech artist and designer who also created the cover for Elías’ book entitled Matematické dílo Bernarda Bolzana ve světle jeho rukopisů (Bernard Bolzano’s mathematical work in the light of his manuscripts). It combines classic and modern fonts, which captures the nature of the project, while introducing a geometric element that highlights the central role of mathematics.
The project “Normalisation and emergence: rethinking the dynamics of mathematics. The case of Prague in the first half of the 19th century” (i.e. PragMatika) is funded by the Czech Science Foundation through the Junior Star grant no. 23-06540M.
