The demands of university teaching, addressed to students … with [only] a modest (and frequently less than modest) mathematical baggage, led me to … start from an intuitive baggage common to everyone, independent of any technical language used to express it, and anterior to any such language—it turned out that the geometric and topological intuition of shapes, particularly two-dimensional shapes, formed such a common ground. These themes can be grouped under the general names “topology of surfaces” or “geometry of surfaces”, … the main emphasis being on the … combinatorial aspects which form the most down-to-earth technical expression of them—and not on the differential, conformal, Riemannian, holomorphic, [Kähler, contact, symplectic, Moishezon] aspects—and from there on to ℂ algebraic curves.
Alexandre Grothendieck, 1988, in a letter to
translated by Michael Barr