Author Description

There Is An Urgent Need In Philosophy Of Mathematics For New Approaches Which Pay Closer Attention To Mathematical Practice. This Book Will Blaze The Trail: It Offers Philosophical Analyses Of Important Characteristics Of Contemporary Mathematics And Of Many Aspects Of Mathematical Activity Which Escape Purely Formal Logical Treatment. Intro -- Contents -- Biographies -- Introduction -- 1. Visualizing In Mathematics -- 2. Cognition Of Structure -- 3. Diagram-based Geometric Practice -- 4. The Euclidean Diagram (1995) -- 5. Mathematical Explanation: Why It Matters -- 6. Beyond Unification -- 7. Purity As An Ideal Of Proof -- 8. Reflections On The Purity Of Method In Hilbert's Grundlagen Der Geometrie -- 9. Mathematical Concepts And Definitions -- 10. Mathematical Concepts: Fruitfulness And Naturalness -- 11. Computers In Mathematical Inquiry -- 12. Understanding Proofs -- 13. What Structuralism Achieves -- 14. 'there Is No Ontology Here': Visual And Structural Geometry In Arithmetic -- 15. The Boundary Between Mathematics And Physics -- 16. Mathematics And Physics: Strategies Of Assimilation -- Index Of Names -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z. Paolo Mancosu. Includes Bibliographical References And Index.