The “universal grammar” of space: what geometry is innate‪?‬ Opinionated History of Mathematics

Geometry might be innate in the same way as language. There are many languages, each of which is an equally coherent and viable paradigm of thought, and the same can be said for Euclidean and non-Euclidean geometries. As our native language is shaped by experience, so might our “native geometry” be. Yet substantive innate conceptions may be a precondition for any linguistic or spatial thought to be possible at all, as Chomsky said for language and Kant for geometry. Just as language learning requires singling out, from all the sounds in the environment, only the linguistic ones, so Poincaré articulated criteria for what parts of all sensory data should be regarded as pertaining to geometry.