Synthetic philosophy of contemporary mathematics

Description

A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. Abstract: A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest Content: Intro Contents Introduction: Options Traditionally Available to Mathematical Philosophy, and a Prospectus of the Essay Part 1: The General Environment of Contemporary Mathematics Chapter 1: The Specificity of Modern and Contemporary Mathematics Chapter 2: Advanced Mathematics In the Tracts of Mathematical Philosophy: A Bibliographical Survey Chapter 3: Toward a Synthetic Philosophy of Contemporary Mathematics Part 2: Case Studies Chapter 4: Grothendieck: Forms of High Mathematical Creativity Chapter 5: Eidal Mathematics: Serre, Langlands, Lawvere, Shelah Chapter 6: Quiddital Mathematics: Atiyah, Lax, Connes, KontsevichChapter 7: Archeal Mathematics: Freyd, Simpson, Zilber, Gromov Part 3: Synthetic Sketches Chapter 8: Fragments of a Transitory Ontology Chapter 9: Comparative Epistemology and Sheafification Chapter 10: Phenomenology of Mathematical Creativity Chapter 11: Mathematics and Cultural Circulation Index of Names