 Geometry has been a school of systematic logical thinking, with Euclid’s work taken to be the paradigm of a well-founded science for millennia, but with a sudden change of views around 1900. It has also been a place of privilege for the elaboration of mathematical methods, from synthetic to analytic treatments, algebraic developments, the rise of structuralism, and more. Contemplating the development of geometry through the ages, one can see how it started as the study of figures (and their measurement) to become the study of space, and ended up being the study of spatial structures – from the most basic topology, to n-manifolds, to the geometries picked up by physicists.