Modernity – language – mathematics. A history of the controversy surrounding the foundations of the discipline and the subject of formal systems. (Moderne – Sprache – Mathematik. Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Sprache.) (German) Zbl 0978.00009

Frankfurt a. M.: Suhrkamp Verlag. 640 S. (1990).
From the author’s introduction (translated from the German): From a mathematical-historical viewpoint we give a novel interpretation of the so-called ‘foundational crisis’ of mathematics; this is not so much a crisis of foundations, but rather a radical reformulation of the concepts of truth, meaning, object and existence of mathematics. Our intention is not only to give a new interpretation of an important part of the history of mathematics, but also to contribute to a better understanding of modernity in its more general social-historical and cultural-historical aspects.
Contents: 1. Prelude: Elements of modernity (beyond the 19th century); 2. The new paradise: freedom, creativity, productivity (Hilbert); 3. Countermodernity: finiteness and intuition (Klein, Poincaré and Brouwer, after Kronecker); 4. Continuing stories (four examples: the foundational crisis, computer science, ideology of National Socialism, Bourbaki); 5. The modernization of mathematics around 1900 (institutional aspects); 6. Discourse and language of mathematics: an attempt (a theoretical chapter which explains the preceding ones); 7. Mathematics in the modern era: speculations (other aspects: artificial languages, Taylorism, biometrics, art).
The book contains a bibliography of 30 pages, an author index and a subject index.


00A30 Philosophy of mathematics
00-02 Research exposition (monographs, survey articles) pertaining to mathematics in general
01A05 General histories, source books