Logos and Alogon : Thinkable and the Unthinkable in Mathematics, from the Pythagoreans to the Moderns

1 The Ghost and the Spirit of Pythagoras in Modern and Modernist Mathematics.- 2 Plato's Ghosts: Pythagorean Mathematics, Socratic Philosophy, and Tragic Art.- 3 'Comprehending the Connection of Things': Bernhard Riemann and the Architecture of Mathematical Concepts.- 4 What is a Curve?: From Geometry to Algebra, from Modern to Modernist Mathematics.- 5 Returns of Geometry: From the Pythagoreans to Mathematical Modernism and Beyond.- 6 Who Thinks Abstractly: Emmy Noether and Modernist Mathematics.- 7 Mathematical Practice as Philosophy, with Galois, Riemann, Poincaré, and Grothendieck.