Periodic Reporting for period 1 - LEGITIMATH (Teaching and learning practices calculus in the 18th century: the case of Italian mathematics and its European dimension)
Período documentado: 2022-02-01 hasta 2024-01-31
The aim of this project was to reevaluate the history of mathematics in 18th-century Europe, focusing specifically on the local dynamics of teaching and learning analytic and synthetic geometry, as well as infinitesimal analysis. The project examined significant locations in the Italian peninsula between 1720 and 1750, both in public and private settings. The ultimate objective was to develop a methodological framework that could be adapted to various cultural and geographical contexts.
The initial phase involved a thorough examination of manuscript notes from Venice, Padua, Verona, and Treviso regarding mathematics instruction at the University of Padua during the first half of the 18th century. The second phase delved into the contributions of women in mathematics during the same period, emphasizing the unpublished manuscripts of Maria Gaetana Agnesi and collaborating with the Accademia dei Concordi in Rovigo on the editing of lectures by Cristina Roccati.
The discovery of previously untapped sources confirmed that algebra and calculus were primarily taught outside of university settings, through private lessons. This raised the unresolved question of the transition of these disciplines from private to public contexts, as well as the impact of these social changes on the content, presentation, and methods of these disciplines. The survey of library archives led to the identification of a larger collection of manuscript notes than initially estimated, providing a valuable archive for future exploration and significantly contributing to our understanding of mathematical education in the early modern period.
The initial phase involved a thorough examination of manuscript notes from Venice, Padua, Verona, and Treviso regarding mathematics instruction at the University of Padua during the first half of the 18th century. The second phase delved into the contributions of women in mathematics during the same period, emphasizing the unpublished manuscripts of Maria Gaetana Agnesi and collaborating with the Accademia dei Concordi in Rovigo on the editing of lectures by Cristina Roccati.
The discovery of previously untapped sources confirmed that algebra and calculus were primarily taught outside of university settings, through private lessons. This raised the unresolved question of the transition of these disciplines from private to public contexts, as well as the impact of these social changes on the content, presentation, and methods of these disciplines. The survey of library archives led to the identification of a larger collection of manuscript notes than initially estimated, providing a valuable archive for future exploration and significantly contributing to our understanding of mathematical education in the early modern period.
In the first specific objective (SO1), I examined key sites in the Italian peninsula (1720-1750), focussing on the lecture notes by Giovanni Poleni at Venice National Library. In the State Archives of Venice, I explored university administration documents. In Treviso, I collected analysis lessons by Jacopo Riccati. At Padua's university library, I reviewed printed sheets of courses by Giuseppe Suzzi and Giovanni Poleni. In Verona, I examined manuscript lectures by Giuseppe Suzzi and Giovanni Poleni. In Milan, Maria Gaetana Agnesi's student notes were consulted, offering insight into the education of a woman mathematician.
In the second year, I studied the circulation of teaching practices in higher mathematics in the early-modern European Republic of Letters. Collaborating with colleagues, we edited a collective volume on algebra and calculus circulation in Italy and Spain during the 18th century. A conference at Ca' Foscari in June 2023 united experts, with a subsequent publication in the History of Universities series (Oxford University Press), represents the final deliverable of this objective.
For training, I received instruction in Research Methodology in intellectual history, history of mathematics, and mathematical education through various means: workshops and conferences organized by the Department of Philosophy and Cultural Heritage in Venice, and the Center for Renaissance and Early Modern Thought (CREMT) at Ca' Foscari. I attended conferences on the history of mathematics education and intellectual history. At the Sarton Centre, where my secondment took place, I underwent additional training to enhance my understanding of the history of philosophy and science in Italy and Europe from the Renaissance to the 18th century. This included improving my writing and argumentative skills, networking, attending seminars, workshops, and conferences organized by the Sarton Centre in the history of science.
A seminar for philosophy students at Ghent university, and an online presentation for teachers and students of the "Liceo Matematico" (high school specialized in mathematics) enhanced my teaching methodologies for a varied public.
Organization of activities (meetings and conferences) that acknowledge the support of the European Community:
- Invited lecture (online): Paolo Mancosu, How many points are in a line segment? From Grosseteste to numerosities (01/0/6/2022).
- Conference (co-organized with prof. Marco Sgarbi): The crisis of the traditional structure of knowledge: teaching and learning mathematical sciences in the eighteenth century, 10 international speakers, 21-22 June 2023.
I also attended and presented papers at several international conferences attended (that acknowledge the support of the European Community), connected to SO1 and SO2. Among the most prestigious ones:
a) Participation to ESU 9th EUROPEAN SUMMER UNIVERSITY ON THE HISTORY AND EPISTEMOLOGY IN MATHEMATICS EDUCATION, 18-22 July 2022, Salerno, Italy, 22 july 2022.
b) “Private and public teaching of mathematics in Padua”, ISIH (International Society for Intellectual History) conference, Venice, 12-15 september 2022.
c) “Teaching mathematics in the 18th century Veneto: the case of Padua”, talk given at the Seventh International Conference on the History of Mathematics Education (ICHME-7) University of Mainz, (Germany), 19. – 23. September 2022.
d) "Teaching mathematics in 18th century Padua: from the Ancients to the Moderns”, talk given at a symposium co-organized with David Mcomish (Ca’ Foscari University, Venice) and Angela Axworthy (MPIWG, Berlin) in Scientiae Congress, Prague, 06/06/2023 – 10/06/2023.
e) “Leibniz on the impossibility of squaring the hyperbola”, talk given at the Leibniz Kongress 2023, 30/07/2023 – 04/08/2023.
In the second year, I studied the circulation of teaching practices in higher mathematics in the early-modern European Republic of Letters. Collaborating with colleagues, we edited a collective volume on algebra and calculus circulation in Italy and Spain during the 18th century. A conference at Ca' Foscari in June 2023 united experts, with a subsequent publication in the History of Universities series (Oxford University Press), represents the final deliverable of this objective.
For training, I received instruction in Research Methodology in intellectual history, history of mathematics, and mathematical education through various means: workshops and conferences organized by the Department of Philosophy and Cultural Heritage in Venice, and the Center for Renaissance and Early Modern Thought (CREMT) at Ca' Foscari. I attended conferences on the history of mathematics education and intellectual history. At the Sarton Centre, where my secondment took place, I underwent additional training to enhance my understanding of the history of philosophy and science in Italy and Europe from the Renaissance to the 18th century. This included improving my writing and argumentative skills, networking, attending seminars, workshops, and conferences organized by the Sarton Centre in the history of science.
A seminar for philosophy students at Ghent university, and an online presentation for teachers and students of the "Liceo Matematico" (high school specialized in mathematics) enhanced my teaching methodologies for a varied public.
Organization of activities (meetings and conferences) that acknowledge the support of the European Community:
- Invited lecture (online): Paolo Mancosu, How many points are in a line segment? From Grosseteste to numerosities (01/0/6/2022).
- Conference (co-organized with prof. Marco Sgarbi): The crisis of the traditional structure of knowledge: teaching and learning mathematical sciences in the eighteenth century, 10 international speakers, 21-22 June 2023.
I also attended and presented papers at several international conferences attended (that acknowledge the support of the European Community), connected to SO1 and SO2. Among the most prestigious ones:
a) Participation to ESU 9th EUROPEAN SUMMER UNIVERSITY ON THE HISTORY AND EPISTEMOLOGY IN MATHEMATICS EDUCATION, 18-22 July 2022, Salerno, Italy, 22 july 2022.
b) “Private and public teaching of mathematics in Padua”, ISIH (International Society for Intellectual History) conference, Venice, 12-15 september 2022.
c) “Teaching mathematics in the 18th century Veneto: the case of Padua”, talk given at the Seventh International Conference on the History of Mathematics Education (ICHME-7) University of Mainz, (Germany), 19. – 23. September 2022.
d) "Teaching mathematics in 18th century Padua: from the Ancients to the Moderns”, talk given at a symposium co-organized with David Mcomish (Ca’ Foscari University, Venice) and Angela Axworthy (MPIWG, Berlin) in Scientiae Congress, Prague, 06/06/2023 – 10/06/2023.
e) “Leibniz on the impossibility of squaring the hyperbola”, talk given at the Leibniz Kongress 2023, 30/07/2023 – 04/08/2023.
During the project, my research expanded to include elementary mathematics. This shift resulted from a survey of primary sources revealing that "modern" infinitesimal analysis wasn't part of the curriculum at the University of Padua. Instead, the university emphasized elementary geometry. The archives in the Biblioteca Marciana in Venice yielded a larger collection of manuscript notes than estimated, particularly those of Giovanni Poleni (1683-1761).
Library archives revealed untapped sources, including Giuseppe Suzzi's lecture notes in Venice and Verona. In Treviso, I consulted Jacopo Riccati's manuscript lessons. While not all sources were studied during the research, they form a valuable archive for future exploration.
Based on case studies during the fellowships, I developed a potential adaptable methodological framework for exploring mathematical education discussion, dissemination, and debate:
Understanding Emergence of Modern Mathematical Education: Examining how mathematical knowledge was disseminated in public forums such as coffee houses and scientific societies. For instance, Roccati's lectures at Accademia dei Concordi.
Examining the Role of Print Media: Studying textbooks and articles to understand taught concepts and accessibility. I focused on French textbooks in the Republic of Venice, particularly authors Tacquet, Dechales, and Ozanam in Poleni's teaching notes.
Analyzing Discourses: Examining debates about the importance of learning mathematics. Evidence from institutional documents, like letters between teachers and authorities, provides insights into curriculum reforms.
Exploring the Intersection of Public and Private: Understanding the role of mathematics in the public and private spheres, considering state intervention and the status of mathematics in universities.
Investigating Issues of Inclusion and Exclusion: Examining who had access to mathematical education. Considering social status, gender, and race to understand exclusionary practices in the 18th century.
Library archives revealed untapped sources, including Giuseppe Suzzi's lecture notes in Venice and Verona. In Treviso, I consulted Jacopo Riccati's manuscript lessons. While not all sources were studied during the research, they form a valuable archive for future exploration.
Based on case studies during the fellowships, I developed a potential adaptable methodological framework for exploring mathematical education discussion, dissemination, and debate:
Understanding Emergence of Modern Mathematical Education: Examining how mathematical knowledge was disseminated in public forums such as coffee houses and scientific societies. For instance, Roccati's lectures at Accademia dei Concordi.
Examining the Role of Print Media: Studying textbooks and articles to understand taught concepts and accessibility. I focused on French textbooks in the Republic of Venice, particularly authors Tacquet, Dechales, and Ozanam in Poleni's teaching notes.
Analyzing Discourses: Examining debates about the importance of learning mathematics. Evidence from institutional documents, like letters between teachers and authorities, provides insights into curriculum reforms.
Exploring the Intersection of Public and Private: Understanding the role of mathematics in the public and private spheres, considering state intervention and the status of mathematics in universities.
Investigating Issues of Inclusion and Exclusion: Examining who had access to mathematical education. Considering social status, gender, and race to understand exclusionary practices in the 18th century.