This is a Consolidator grant 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€ //  Start: October 1, 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:

    1. Develop a fallibilist theory of mathematical justification and knowledge.
    2. Explore the interdependence between knowledge-that and knowledge-how in mathematics by focusing on how mathematicians use notations and diagrams.
    3. 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.

Collaborators:
  • Jeremy Avigad (Department of Philosophy and Department of Mathematical Sciences, Carnegie Mellon University, USA) — on Research Objective 3
  • Laura Branchetti (Department of Mathematics, University of Milan) — on the application for mathematics education
  • Jessica Carter (Department of Mathematics, Aahrus Univerisity, Denmark) — on Research Objective 2
  • Axel Gelfert (Institute of History and Philosophy of Science, Technology, and Literature, Technical University of Berlin, Germany) — on Research Objective 1 and 2
  • Roberto Natalini (Institut for Applied Mathematics “Mauro Picone,” CNR, Rome) — on outreach
  • Andrea Sereni (Class of Human and Life Sciences, IUSS Pavia) — on Research Objective 1