Mysticism, number, and geometry : an introduction to Pythagoreanism -- The Elgin Marbles and Plato's geometric chemistry -- An introduction to infinity -- The flat Earth and the spherical sky -- Theology, logic, and questions about angels -- Time, infinity, and incommensurability -- Medieval theories of vision and the discovery of space -- The shape of space and the fourth dimension -- What is a number? -- The dual nature of points and lines -- Modern mathematical infinity -- Elegance and truth.