Research
1. Autonomy's End? AI and Crises of Mathematics in the 21st Century
The project investigates the epistemological transformation of mathematical cultural practices due contemporary AI-generated mathematics. Such cultural practices can be reading, writing but also drawing; digital technologies have fundamentally altered such practices, and I focus on recent AI-based systems. Starting with the plurality of visualizations of mathematical objects in the 19th and 20th century, as seen, for example, with two-dimensional diagrams or three-dimensional models, my research aims uncovering their role in mathematical discovery in the 21st century AI-shaped mathematics (see my co-edited volume Model and Mathematics, 2022; ed. with Karin Krauthausen). Continuing my research on the history of folding practices in mathematics (A History of Folding in Mathematics, 2018), my coming work on disappearing materiality examines the algorithmic transformation of mathematical material, textual and visual practices, establishing the theoretical foundation for my current project on AI-generated mathematical texts and imagery (see my latest publication and my recent work on mathematical intuition in the Age of AI). Such work aims as well to uncover how mathematical writing and reading have been radically transformed due to such developments.
* Coming: In the framework of this research, I am happy to announce that during 2027 I will be a NOMIS Fellow at eikones – Center for the Theory and History of the Image in Basel, Switzerland, with my project "The Second Crisis of Mathematical Visualization: From 1960s Computer-Generated Images to the 2020s Al-Generated Diagrams".
* In this framework, Dr. Deborah Kent (University of St Andrews) and I have won the University of St Andrews and University of Bonn Collaborative Research Grant on “On Proofs and Partnerships: How AI, Big Data, and Proof Assistants are Transforming Mathematical Practices” for 2026-27 (ca. 22,000 Euro)
A braid diagram represeting a plane curve of degree 6 with six cusps, all of them lie on a conic (Dedò, Modesto. 1950. “Algebra delle trecce caratteristiche: Relazioni fondamentali e loro applicazioni”, p. 257)
2. Material Epistemologies
My research on material epistemology examines how materials and artisanal practices like folding and weaving historically shaped scientific thought (see my books A History of Folding in Mathematics (2018) and On Joachim Jungius’ Texturæ Contemplatio (2023)). In the former, I have traced the marginalization of folding as a mathematical practice from the 16th to 20th centuries, distinguishing between material practices as epistemic and a technical, hence demonstrating how this duality influenced the exclusion of such practices from mainstream scientific discourse. For instance, while Albrecht Dürer’s polyhedral nets leveraged folding’s material logic, later mathematicians dismissed it as pedagogically limited or artistically trivial. I aim to highlight, to give one example, how 19th-century educators like Friedrich Fröbel reconceptualized folding as a tactile pedagogical method, bridging German Idealist philosophy and crystallography. This tension between haptic experimentation and formal symbolism, I contend, reflects broader historical shifts in how material practices inform abstract knowledge.
On Joachim Jungius’ Texturæ Contemplatio (2023) deciphers Joachim Jungius’ 17th-century manuscript to explore how weaving technologies influenced natural philosophy in the Early Modern Period. Jungius analyzed textiles through various scientific frameworks, classifying weave structures geometrically or investigating their optical properties under microscopes. I question whether this work should be considered as a ‘trading zone’ between artisans and scholars, where textile metaphors permeated ontological debates. Jungius’ attempts to codify weaving reveal how Early Modern thinkers sought to reconcile empirical craftsmanship with scientific reasoning, yet his manuscript remained unpublished, emblematic of the era’s struggle to legitimize material epistemologies. Together, these works underscore a central thesis: artisanal practices are not mere precursors to formal knowledge but constitutive of its evolution, challenging narratives that privilege disembodied abstraction over material ingenuity.
* In this framework, I won the ISF (Israel Science Foundation) Grant: “Expanding Geometry in the 17th century: A Migration of Knowledge from Weaving to Mathematics?” (2021-2025): ca. 90,000 Euro
A drawing of interlaced threads from Jungius’ Texturæ Contemplatio, fol. 33r; © Gottfried Wilhelm Leibniz Bibliothek - Niedersächsische Landesbibliothek.
3. Mathematics in the 21st Century and the New Regimes of Linguistic Purity
Taking the previously unexplored relationship between Hans Blumenberg, the influential German philosopher and historian of ideas, and mathematics, as a starting point, the project claims, that despite there being no articles or books in which he deals specifically with mathematical topics, Blumenberg’s published and unpublished manuscripts reveal sophisticated reflections on mathematics, its history and philosophy. This is the project's starting point: with Blumenberg, I aim to trace how his metaphorological investigations and their rejection of the Cartesian project of clarity and purity can shape a new epistemological conception of mathematics in the 21st century, which is being more and more reshaped by AI-based technologies and automatic proof assistants (on anxiety in the mathematical discourse due to such technologies, see here). Blumenberg reveals mathematics as historically contingent and shaped by nonconceptual elements that resist complete formalization. Alongside a consideration of the various chapters framing the appearance of impossibility, ambiguity, and anxiety in mathematical discourse in the 20th and 21st century, the investigation of Blumenberg’s historical-philosophical ‘mathematical detours’ opens, as the project will show, new horizons in the philosophy of mathematics by emphasizing the irreducible metaphoric foundations underlying mathematical concepts and their development. My upcoming monograph Hans Blumenberg, Mathematical Non-Conceptuality, and the Failed Search for Linguistic Purity in the 20th Century (2027) will be the starting point of this project.