RECENT OUTPUTS
E. Fuentes Guillén, Matematické Dílo Bernarda Bolzana ve světle jeho Rukopisů, Filosofia, Praha, 2023, 978-80-7007-742-9.
Kniha je věnována vývoji matematického myšlení Bernarda Bolzana ve světle jeho posmrtně vydaných i dosud nepublikovaných rukopisů. Každá kapitola se zaměřuje na jiné aspekty – první kapitola se zabývá pozadím vzniku rukopisu, v němž je odhaleno, co sám Bolzano považoval na svých Beyträge za nejpozoruhodnější, druhá se zaměřuje na pojem proměnných veličin ω a třetí na Bolzanovu teorii čísel. Bolzanův přínos v oblasti matematiky, jejích základů a metodologie, je nesporný, svědčí však také o nejistotách a napětí, částečně způsobených jeho lpěním na zděděných koncepcích a postupech. Bolzano tak představuje průkopnickou osobnost, jejíž studium je důležité pro lepší pochopení praktických a koncepčních změn, jimiž prošla matematika v 19. století.
Crippa D., Massa-Esteve, M. R. The algebrization of mathematics during the 17th and 18th centuries. Dwarfs and giants, centres and peripheries. College Publication, 2023, 978-1-84890-394-4.
This book explores the major historical phenomenon of the algebraization of mathematics in the second half of the 17th and 18th centuries, offering a broader understanding of the consolidation of analytic geometry and infinitesimal calculus as disciplines. The authors examine the external (intellectual, geographical, and political) factors that influenced these transformations and shed light on the process of acquisition and integration of analytical mathematics into traditional curricula. Drawing on new trends in historiography of science, this book emphasizes the importance of "dwarfs", that is mathematicians but also technicians, artisans, military personnel, engineers, and architects, often ignored or marginalized in traditional histories, in the circulation of original mathematical knowledge, and of peripheral countries such as Italy and Spain as important sites for the appropriation and production of such knowledge.
Davide Crippa. Teaching Elementary Mathematics at the University of Prague: A Study of Latin Compendia from the Second Half of the 18th Century, Almagest, 13, 1, 80-141, 2022.
https://doi.org/10.1484/J.ALMAGEST.5.131490
From the middle of the 18th century on, the central authority in Vienna strove to increase its control over education in the Habsburg lands, attempting to introduce a series of reforms in university education in order to modernize the curricula in lower and higher educational institutions, institutions in which the influence of the Jesuits was predominant until the Society of Jesus’s suppression by the Pope in 1773. A consequence of these reforms was that the teaching of mathematics changed significantly in Habsburg territories between circa 1750 and 1784.
In this paper, we shall survey the content and structure of the course in Elementary Mathematics at the Charles-Ferdinand University in Prague. The teaching of mathematics at this college, which is fairly well documented, represents a fruitful case study for assessing the circulation of modern ideas in mathematical teaching. These ideas were promoted by contemporary authors like Christian Wolff or Nicolas Louis de la Caille, and were assimilated by the local scholarly community.
Fuentes Guillén, E., Bolzano on Bolzano: A Hitherto Unknown Announcement of Bolzano’s Beyträge, History and Philosophy of Logic, 2022.
https://doi.org/10.1080/01445340.2022.2147750
In 1817, in the preface to his Rein analytischer Beweis, Bernard Bolzano revealed that he had decided to postpone the publication of any subsequent instalment of his Beyträge zu einer begründeteren Darstellung der Mathematik because of the few and ‘superficial’ reviews of its first instalment, published in 1810. Bolzano’s transcriptions of the only two known reviews of this book are conserved at the Literární archiv Památníku národního písemnictví / Muzea literatury, in Prague, together with another manuscript on his Beyträge, the provenance of which was unknown to Bolzano’s scholars until recently. In this paper it is shown that this latter manuscript is a draft of an announcement that was published at the time and that was indeed written at least to some extent by Bolzano himself. This hitherto unknown announcement of Bolzano’s Beyträge not only solves the mystery surrounding that manuscript, but also helps to date the publication of this book more precisely and provides an unusual insight into what we must take Bolzano himself to have considered most noteworthy about his work, namely his study on logic. The paper includes a transcription of the manuscript and an English translation of the announcement.
Fuentes Guillén, E., Crippa, D.The 1804 examination for the chair of Elementary Mathematics at the University of Prague. Historia Mathematica, 57, 24-54.e18, 2021.
In 1804 the chair of Elementary Mathematics at Prague University became vacant and a selection procedure, which consisted of a written and an oral examination, was announced. Only Bernard Bolzano and Ladislav Jandera took part in it. Jandera was appointed to the chair, whereas Bolzano became Professor of “Religious Doctrine.” In this paper we examine the context of this Concursprüfung, the performance of both candidates and the outcome, based on a number of related papers preserved at the Czech National Archives. In addition to this, we publish for the first time, albeit only in the online version of this paper, the transcription and English translation of Bolzano's written examination.
All the publications issued during the project are listed at STARFOS
Institute of Philosophy
Czech Academy of Sciences
Jilská 1
110 00 Prague 1
Czech Republic
crippa@flu.cas.cz