TITLE: Mathematicians with aphantasia (inability to visualize things in one's mind)
QUESTION [44 upvotes]: Are there any mathematicians with aphantasia? If so, could they please elaborate upon what their experience with mathematics is like?
I realize that this question probably falls outside of the scope of Mathoverflow, but it's so shocking that such a fundamental mental difference exists that I think the question is worth asking here anyways. Even if it gets closed, which I suspect it will, if even one mathematician with aphantasia sees this and has the startling revelation that they have aphantasia, I'll be 1000000% glad I posted the question.
*inability to visualize things in one's mind. see this note that went viral recently for a more detailed explanation: https://www.facebook.com/notes/blake-ross/aphantasia-how-it-feels-to-be-blind-in-your-mind/10156834777480504

REPLY [3 votes]: I do not think I have aphantasia, but I want to point out that "mental imagery" is very different from an image that you are directly looking at.  Consider a map of the world.  If you ask me to mentally visualize a map of the world, I believe I can do so, but if you then ask me, "Does China share a border with Kyrgyzstan?" I can't answer that question by just "looking at that part of the map" and getting the answer, which I certainly could do if I were looking at an actual (political) map of the world.  My geographical knowledge of that part of the world is somewhat fuzzy and so my mental image is fuzzy, but it's not fuzzy in the way that an actual blurred visual image is fuzzy.  Furthermore, even when I fancy that I can mentally "see" a border, such as the border between the U.S.A. and Canada, you can easily ask me difficult questions that I can't answer using my "mental image" that I could trivially answer by looking at an actual map.
I have also noticed many people talking about "visualizing" 3-dimensional space, but surely this is another example of a clear difference between mental imagery and actual visual images.  At best, we literally see only two spatial dimensions.  Three-dimensional space is something we conceptually construct, not something we see directly. I'd go further and say that even our mental "images" of two-dimensional projections of three-dimensional objects are quite different from actual two-dimensional images. Take for example the old puzzle where we take a square-based pyramid with equilateral triangles as faces and we glue a regular tetrahedron to one of the faces of the pyramid.  I think I can form a mental image of this object, but suppose you ask me whether it has 7 faces or 5 faces.  With the actual object, if you were unsure, you could just pick it up, look at it from an appropriate angle, and see that the faces are flush.  But with a mental image, if you are unsure, you probably cannot solve the problem just by "looking."  You probably have to think about it and work it out.
All this is to say that I have doubts about how much the ability to conjure up "mental imagery" helps mathematical thinking.  For those with the ability, I am sure it helps to some extent, but I suspect that it helps less than it might seem, and that much of what we attribute to our ability to form mental images is actually a far more complex process than (ahem) meets the eye.