This book offers the first in-depth investigation of the mathematical dimension of Hans Blumenberg’s thought.

Hans Blumenberg is not usually considered as a philosopher or historian of mathematics. Yet throughout his unpublished manuscripts, notebooks, annotated books but also in some of his published writings, mathematics emerges as a persistent and revealing concern.  Unfolding his engagement with mathematics from the 1950s through the 1980s, the book traces the connections between mathematical concepts, metaphor, non-conceptuality, and the history of ideas. It shows how Blumenberg’s reflections about mathematics – his discussions of riddles, paradoxes, impossibilities, crises, and mathematical-linguistic spaces – challenge the familiar image of mathematics as a timeless, autonomous, and transparent discipline. Against projects that seek to purify language and eliminate ambiguity, Blumenberg reveals mathematics as a historically contingent, human, and metaphorically laden practice.

Drawing on archival materials from Blumenberg’s literary estate, the book examines his reflections on various mathematical concepts and domains. Moreover, it situates these reflections together with Blumenberg’s own dialogue with Edmund Husserl and Ludwig Wittgenstein; in doing so, it uncovers both a distinctive philosophy of mathematics and a unique view of its history, in which mathematical concepts remain grounded in a nonconceptual domain that resists complete formalization. It is for this reason that for Blumenberg, the search for linguistic and mathematical purity in the 20th century is a failed one. This study therefore not only establishes mathematics as an important, though neglected, strand in Blumenberg’s writings; it also opens new perspectives on the history and philosophy of mathematics. By attending to metaphors, riddles, and anxieties surrounding mathematical change, it offers a historically sensitive account of how mathematical concepts emerge, transform, and acquire meaning.

The book is essential reading for researchers of Hans Blumenberg, the history and philosophy of mathematics, and the history of ideas. It is also ideal for scholars of philosophy, intellectual history, history of science, and metaphor studies.

Michael Friedman is a research associate at the University of Bonn and a historian of mathematics, focusing on the history of mathematics and mathematization processes in the 20th century as well as on the history of AI-produced mathematics.