The architecture of modern mathematics: Essays in history and philosophy

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INTRODUCTION REINTERPRETATIONS IN THE HISTORY AND PHILOSOPHY OF FOUNDATIONS Frege and the role of historical elucidation: Methodology and the foundations of mathematics Riemann's Habilitationsvortrag at the crossroads of mathematics, physics and philosophy The Riemannian background to Frege's philosophy Axiomatics, Empiricism, and Anschauung in Hilbert's conception of geometry: Between arithmetic and general relativity EXPLORATIONS INTO THE EMERGENCE OF MODERN MATHEMATICS Methodology and metaphysics in the development of Dedekind's theory of ideals Emmy Noether's set-theoretic topology: from Dedekind to the rise of functors Tarski on models and logical consequence A path to the epistemology of mathematics: Homotopy theory ALTERNATIVE VIEWS AND PROGRAMS IN THE PHILOSOPHY OF MATHEMATICS Felix Hausdorff's 'considered empiricism' Practice-related symbolic realism in H. Weyl's mature view of mathematical knowledge From Kant to Hilbert: French philosophy of concepts in the beginning of the 2

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