I am trying to think of geometry in a pedagogical context and in particular, to what extent "geometric intuition" is a built-in part of our brain (and to what extent is it earned through experience). Naturally I want to understand how this works in algebraic geometry, where you usually can think of something either algebraically or geometrically.
My question is then do people who were blind from birth and consider themselves algebraic geometers (in the course of their work) actually see nice pictures of lines, surfaces, and curves in their heads? Or do they see Cohen-Macaulay rings and injective resolutions etc.? If it is the former that indicates that "geometric intuition" is built-in.
Among the general algebraic geometer population, it is apparently the former but since blind people are a minority it is impossible to draw conclusions about them from the linked survey: https://mathoverflow.net/a/86184