The University School for Advanced Studies IUSS Pavia is pleased to announce that Silvia De Toffoli has been awarded a prestigious grant from the Italian Science Fund for her research project HUMATH – Humanizing Mathematical Knowledge: Fallibility, Technology, Know-How. The three-year project was selected in the “Consolidator” category from a large pool of applications in a highly competitive selection process.

HUMATH investigates mathematical knowledge from an innovative perspective, highlighting its human dimension and, in particular, its historical and practical aspects. Traditionally, the philosophy of mathematics has focused on foundational and ontological questions, overlooking the way mathematics is actually practiced. HUMATH fills this gap through an interdisciplinary analysis that engages both mathematics itself and mathematics education. It explores the fallibility of mathematical knowledge, the essential role of notations and diagrams in knowledge acquisition, and the impact of computational tools and artificial intelligence on mathematical practice. The project aims to redefine our understanding of mathematics—not as a static body of immutable truths, but as a deeply human and continuously evolving activity.

The project has three research objectives:

1. To develop a fallibilist theory of mathematical justification and knowledge.

2. To explore the interdependence between knowledge-that and knowledge-how in mathematics by focusing on how mathematicians use heterogeneous notational systems, including diagrammatic notational systems.

3. To examine the different roles that computers play in mathematical research, focusing on how diagrams and other visual representations can be integrated within interactive proof assistants.

Its contributions will be mainly in the philosophy of mathematics, epistemology, mathematics education, and the communication of mathematics.