Reflections on the Nature of Mathematics
(Download links coming slowly.)
Part I: Activity of Mathematics
§ Games: technical, logical-rational, phronetic-aesthetic§ Modes: science of objects, game of rules
§ Structure and Narrative: space and time
§ Abstract and Concrete
§ Five Archetypes: composer, performer, teacher, philosopher, puzzle-solver
Part II: Art of Mathematics: music, language, code
§ Standard of Judgment: learning to play proofs§ Technique
§ Depth Grammar
§ Translation
§ Meaning
§ Exercise
§ Education
Part III: Character of Mathematics
§ Ingredients: metaphysics, language, puzzles§ Beauty and Fetish, Depth and Complexity
§ Things and Parts
§ Analysis and Synthesis
§ Layers and Texture
§ Visibility
§ After Infinity
Part IV: Evolution and Revolution of Mathematics
§ Science and Technology: Revolution and Accretion§ Application
§ Industrialization: light and massive technology
§ Projects, Problems, Programmes
§ Circulation