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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

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    $\begingroup$ I'm in grad school, and a fellow grad student here has aphantasia. She said it makes some things tough but that in general it hasn't affected her too much. And she does geometric topology! I can put her in touch if you want. $\endgroup$ – Kevin Casto Apr 24 '16 at 22:31
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    $\begingroup$ @KevinCasto: wow, geometric topology is about the last discipline i would've guessed one could find someone with aphantasia in. yes, am interested in asking her some questions about math and aphantasia (will shoot you an email on your uchicago adress titled "Aphantasia and Math"). Though, if she's comfortable (& entirely understood if she's not comfortable speaking about such a personal matter / philosophical topic in a public forum) , i imagine there are alot of people other than me who would be curious to read some sort of reply on mathoverflow. $\endgroup$ – Trent Apr 25 '16 at 5:01
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    $\begingroup$ @ManfredWeis: medical term which received a name in an article by Adam Zeman and colleagues in the journal Cortex in 2015 sciencedirect.com/science/article/pii/S0010945215001781 $\endgroup$ – Trent Apr 25 '16 at 5:01
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    $\begingroup$ @KevinCasto: Meanwhile, Antoine (necklace) and Morin (sphere eversion) were blind, though neither from birth, $\endgroup$ – Adam Epstein Apr 25 '16 at 13:03
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    $\begingroup$ Thank you for posting this question. I always thought I am the only person who cannot visualize. It was a great relief to read the article by Blake Ross and to learn that 2 percent of the population have this anomaly too. $\endgroup$ – Johann Cigler Apr 26 '16 at 15:15
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I'm the grad student mentioned above by Kevin Costo. I should give a little disclaimer, which is that I am self-diagnosed based on the VVIT questionnaire. I was reading an article that described aphantasia, and instantly recognized myself in the description.

As Kevin mentioned, I do geometric topology. I find that it doesn't present much of a problem for me, pretty much because I can still keep track of relationships between, say, points - I just don't have a mental image. As an example, in the opening of Thurstons book on 3- manifolds, he talks about what one would see when sitting in a 3-torus and looking around. This, while "visual," made perfect sense to me.

Another example is the game Skribble, in which one person decribes a drawing of a shape (say, a train) using simple geometric shapes (rectangles, circles, etc). The idea is to guess what the shape being described is. I can play this game in my head. How? I don't know, to be honest. I know I don't have a picture in my head, but I sort of know the schematics, how things relate to each other.

I'd say the biggest problem I've run into is when something is sufficiently complicated and I need a sequence of steps to simplify it. If I need to, I just draw a picture. In some ways, I think it may be easier for me to be a geometer than, say, a category theorist, because I've already found ways to think about actual objects and their relationships. I don't have a way to visualize abstract objects.

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    $\begingroup$ Here is Bill Thurston on the example of the blind mathematician Morin and his work on sphere eversion (More Mathematical People, pp. 337-338): "It's something most people have a great deal of trouble visualizing. In fact, I think that vision is somehow distracting to the spatial sense, because we have a spatial sense that is more than just vision. People associate it with vision, but it's not the same. If I close my eyes and imagine what this room is like, I will have a sense in my mind that there's a table here and something here and there. (cont.) $\endgroup$ – Todd Trimble Apr 26 '16 at 1:53
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    $\begingroup$ It will be a sense of the room that doesn't have much to do with perspective. It's hard -- that is, it takes a lot of training -- to go from a spatial image to a picture on paper. So these things are not necessarily stored in our minds in a visual sort of way. We translate what we see into a sense of space. If you think of it, you realize that if you imagine a table with four chairs around it, it doesn't matter whether you can see the seats of the chairs. You just know that they are there. It's kinesthetic as well as visual." MurphyKate, does this at all correlate with your experience? $\endgroup$ – Todd Trimble Apr 26 '16 at 1:54
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    $\begingroup$ Todd - yes, I think that exactly what I'm using. $\endgroup$ – MurphyKate Montee Apr 26 '16 at 2:03
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    $\begingroup$ This is closely related to Todd's question, but I don't know if it is asking about exactly the same sense: When I was learning how to do a 360 front flip, I learned via manipulating my body in certain ways, then mentally simulating how I predicted changes in motion would change how my body moved, executing the changes to the best of my ability, then repeating the cycle until I learned the move. I didn't use visual perception or visual perception in my mind's eye to figure out how my body was moving, I used a kinaesthetic sense of bodily/spatial awareness. I definitely don't have aphantasia, $\endgroup$ – Trent Apr 26 '16 at 5:55
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    $\begingroup$ @trent: yes. I have pretty solid spatial awareness/proprioception. $\endgroup$ – MurphyKate Montee Apr 26 '16 at 23:11
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Though I surely am aphantasmic I can only guess how my mathematical experience differs from that of visualisers since I do not know what visualisers “see” when doing mathematics. I had no problems in studying mathematics but I had to do it in my own way. I learned most things from books or articles since I have difficulties in absorbing information through listening to lectures. To understand an abstract theory I must do many concrete examples or find analogies to already familiar theories in order to get a “feeling” of the theory. I think my bad memory or my inability to play chess must also partly be due to my inability to generate images in my head. But perhaps some visualisers also have similar problems.

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Disclaimer: I don't have aphantasia, so this may be irrelevant to your question.

I graduated university with a BS in math and am starting grad school this fall. I am not an aphantasiac, but when I learned about aphantasia I immediately related. My thought process almost never defaults to mental imagery, although I can make wispy, vague mental images with much effort which are gone almost the second they arrive. My thinking is almost completely semantic - dialogue, facts, data, concepts, etc. with no accompanying mental sensation. I actually sense that this is a strength for me. Visual representation, to me, is a huge distraction, especially in mathematics. As the geometric topologist pointed out, the way things (whether that be actual points in space or concepts) are related to each other, factually, is usually the meat of what you're looking for, and having a mental process that cuts right to that without any middle-man step in between "feels" more efficient. But maybe that's just because it's all I've ever known. I suspect that it's the reason I'm able to mentally handle large amounts of data at a time - because in my head it very rarely comes with any cumbersome (visual or otherwise) attachments.

A more practical example of this is the way I remember driving directions. I don't remember what the road looked like or possess any spatial feel or awareness of what my surroundings were, but I remember a series of facts. Example: pass two stop signs, then turn right... Instead of simply approaching the road and visually remembering, ah, this is where I turn right. I guess in that sense, any time I drive somewhere is like the first time again. I'm giving myself instructions in my head as if I'm giving them to someone else who needs directions.

Ironically, one of my strongest areas in my undergrad was graph theory. I know the factual characteristics of any certain graph, but it comes to my mind unencumbered by the visual representation, and I quite like that. It's more streamlined and "clean" to me. My weakest area was vector calculus; the professor constantly told us to just "see" the dimensions of whatever problem we were working on in the mind's eye. Since the discovery that the strength of one's ability to visualize may exist on a spectrum, I understand why that seemed nearly impossible and so frustrating to me. So it seems that I am more inclined toward anything dealing with relationship (or fact and pattern, like number theory) as opposed to problems dealing with measurement and real-world dimension.

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  • $\begingroup$ exactly my experience, thanks for writing that up! $\endgroup$ – Gytis May 23 '16 at 12:45

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