Book Review: Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, Volume 48, Number 10

In his 1905 essay “L’Intuition et la Logique en Mathématiques”, which appears in translation in [P1], pages 210–222, Poincaré looks at mathematical production from a different angle. He pictures two different kinds of mathematician. One kind is devoted to explicit logical precision. Ideas must be broken down into definitions and deductions. Even conceptions that seem clear and obvious must be subjected to analysis, cut apart, and examined under the microscope of logic. The other kind of mathematician is guided by geometric intuition, physical analogies, and images derived from experience. This mathematician is like Klein, who proved a theorem in complex function theory by imagining a Riemann surface made of metal and considering how electricity must flow through it.