The Historicity of Mathematics as a Philosophical Problem: New Insights

This chapter explores the historicity of mathematics as a philosophical problem. It brings together insights from the history of mathematics, phenomenology, and the philosophy of language to argue that mathematics should be understood as a dynamic, unfolding activity. The works of Jacob Klein (1992), Sabetai Unguru (1975), Reviel Netz (1998; 2022), and Viktor Blåsjö (2016) provide the historiographical foundation of this approach, each challenging the ahistorical conception of mathematics in distinct ways. These perspectives are further enriched by the phenomenological analysis of time offered by Renxiang Liu (2025), whose concept of temporal differentiation provides a novel ontological basis for understanding how mathematical meaning develops. To deepen the philosophical implications, the chapter also engages with the reflections of Ludwig Wittgenstein (1953), Saul Kripke (1982), and Mark Steiner (1998). By integrating these strands, the chapter proposes a new understanding of the historicity of mathematics—one that acknowledges the discipline’s conceptual shifts, philosophical tensions, and cultural embeddedness. Mathematics is not exempt from history but meaningful only within it. Accordingly, the historicity of mathematics is not a peripheral concern for historians or educators, but a central philosophical problem with wide-ranging implications for how mathematics is taught, studied, and understood.