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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

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closed as too broad by Peter LeFanu Lumsdaine, David Roberts, Chris Godsil, Pace Nielsen, Joonas Ilmavirta Aug 12 at 21:23

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Not limited to algebraic geometers or blind from birth: Allyn Jackson, The world of blind mathematicians. $\endgroup$ – Francois Ziegler Aug 8 at 10:55
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    $\begingroup$ Blind-from-birth people having geometric intuition doesn’t at all seem an argument that it’s built-in rather than “earned through experience”: they still have plenty of geometric experience, just through senses other than vision. This question (like many such) seems to be based on fairly naïve speculation about how blindness affects experience and perception: I recommend reading writings by blind authors (or interviews with them, etc) to get a more informed perspective! The article @FrancoisZiegler mentions is a good start — pdf here: ams.org/notices/200210/comm-morin.pdf $\endgroup$ – Peter LeFanu Lumsdaine Aug 8 at 11:43