Francesca Galli receives an SNSF Starting Grant to explore the cultural resonance of geometry in the Middle Ages

Researcher Francesca Galli, lecturer at the Institute of Italian Studies (ISI) of the Faculty of Communication, Culture and Society at Università della Svizzera italiana, has been awarded a Starting Grant from the Swiss National Science Foundation (SNSF) for the project "Tracing the Lines: Geometry's Cultural and Intellectual Resonance in Tuscany (1060–1410)".

The project, scheduled to begin on 1 January 2027, will last for five years and will receive a total funding of CHF 1,680,597. The funding is an important recognition that consolidates the research career of the scholar, who obtained her PhD at USI in 2016 and is currently also a postdoctoral fellow at the University of Zurich (UZH) and holder of an SNSF Ambizione grant.

Geometry as a cultural paradigm
The project aims to explore geometry as a form of multidimensional knowledge during the Western Middle Ages, moving beyond its modern understanding as merely a branch of mathematics.

Through an interdisciplinary approach that combines the history of science, art history, philology and cultural studies, "Tracing the Lines" will investigate the presence and manifestations of geometry from the construction of Pisa Cathedral (c. 1060) to the years immediately preceding the invention of linear perspective (c. 1410).

Using historical-documentary methodologies and transdisciplinary tools for material and formal analysis – including digital ones – the project will examine texts, manuscripts and works of art to understand how geometric knowledge spread and transformed in different areas of medieval thought, thanks in part to the influence of non-Latin traditions such as Arabic, Jewish and Greek.

The primary goal is to view geometry as a multicultural and transmedia paradigm that influences how we conceive and structure thought and artistic expression, fostering both formal coherence and creativity.

An innovative perspective on medieval knowledge
Geometry in the Western Middle Ages was much more than a mathematical discipline: this can be said without forgetting its links with other sciences that were fundamental at the time, such as astronomy and optics.

The intellectual, artistic, and literary output of Tuscany from the 11th to the 15th centuries serves as clear evidence of the importance and prevalence of geometry, along with the various roles it plays within that context.

"Imagine entering a church and hearing about pi and the measurement of the circumference during a sermon," explains Francesca Galli. "That is what would have happened if we had passed through the ancient cathedral of Florence, Santa Reparata, on 20 December 1304. Within a few years, one of the city's most famous citizen, Dante, would compare himself to a 'geometer' faced with the mystery of squaring the circle. And we could cite many other examples: from theologians who find in the properties of the angle of contingency clues to understanding divine mysteries, to the artists of Pisa who may have been inspired by Fibonacci's mathematical 'discoveries' to define the proportions between architectural elements, from ornamental details to the relationships between the spaces of an entire building."

Through a series of case studies, with particular attention to the transcultural dimension (interactions between cultures, languages, and levels of education) and the peculiarities of the different media involved, the project aims to highlight how geometry influences the construction of thought and artistic expression, promoting both rigour and creative freedom.

From optics to geometry: a path of research
"My interest in the 'extraordinary' uses of science in the Middle Ages, "says Galli, "began during my PhD, with the study of De luce, a late 13th-century treatise that relates visible light to otherworldly illumination. In my Ambizione project, I continued to explore references to optics even outside its disciplinary boundaries, for example, in preaching and Dante's commentaries. This line of research led me to question the functions and applications of geometry, whose influence is decisive in many other areas of medieval culture."

Challenges and prospects
"The challenges we will face are numerous; however, the support of a research team with complementary skills, consisting of two doctoral students and a postdoctoral researcher, is a significant advantage. We will be working on unpublished and under-researched material, making the research process dynamic and continually evolving."

The project will culminate in an interdisciplinary conference involving scholars from the fields of psychology, neuroscience and the humanities, accompanied by an exhibition in collaboration with architecture students.

Francesca Galli concludes, "I hope this investigation will help dispel the notion of the Middle Ages as a time of darkness and backwardness. Instead, I aim to highlight this period as one of extraordinary intellectual vitality, where the exact sciences and the humanities engage in meaningful dialogue. Only through a genuine comparison of these fields of knowledge can we achieve a deeper understanding of humanity and foster truly shared progress oriented toward the common good."