Matthew McMillan
mcmillan@virginia.edu

Essays

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

Wittgenstein

Philosophy of Science