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