Taking R G Collingwood’s idea of metaphysics as the study of the changing presuppositions of a science (construed broadly, to include history), what would we include in a study of the presuppositions of geometry? In other words, what would a successor look like to Robert Toretti’s Philosophy of Geometry from Riemann to Poincaré and Jeremy Gray, Ideas of Space: Euclidean, Non-Euclidean, and Relativistic or Worlds Out of Nothing?
Klein, Erlanger Program
Lie,
Poincare
Hilbert
Noether, Alexandrov, algebraic topology
Grothendieck, n-groupoids
Connes, noncommutative geometry
Cartier’s Mad Day’s Work
Other noncommutative geometry
Lurie, Toen, derived algebraic geometry, higher geometry
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