This is a Consolidator grant of the second edition of the FIS Grant, which is considered to be the Italian version of the European ERC Grant.
PI: Silvia De Toffoli, IUSS Pavia // Amount: 1,660,388€ // Expected start: February 2025.
HUMATH — Humanizing Mathematical Knowledge: Fallibility, Technology, Know-How
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 aims to develop an in-depth and interdisciplinary analysis of mathematics in which human subjects come to the fore. HUMATH has three Research Objectives:
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- Develop a fallibilist theory of mathematical justification and knowledge.
- Explore the interdependence between knowledge-that and knowledge-how in mathematics by focusing on how mathematicians use notations and diagrams.
- Investigate 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 in philosophy, mathematics education, and communication of mathematics.
