Some types of synesthesia, mainly the number-related types, can be considered mathematical synesthesias. However, it appears that “pure” mathematical synesthesia – the highly detailed visualisation of actual mathematical concepts – is extremely rare and tends to be either an acquired synesthesia, as a result of brain injury for example, or one of the types normally only found in savants (people with a prodigious talent who are usually on the autism spectrum).

**Here are some types of synesthesia connected to
mathematics**:

1. The
type of synesthesia where **each number has its own unique shape, colour, spatial
position, size and/or personality**, not only one- or two-digit numbers but
**hundreds or thousands of individual numbers.** The writer and high-functioning autistic
savant Daniel Tammet has this very rare type. He
has extraordinary mathematical capabilities: his synesthesia helped him achieve
a record recital of Pi to 22,000 decimal places, as he can use the visual forms
of his numbers to create highly memorable mental landscapes.

“The
number 1, for example, is a brilliant and bright white, like someone shining a
flashlight into my eyes. Five is a clap of thunder or the sound of waves
crashing against rocks. Thirty-seven is lumpy like porridge, while 89 reminds
me of falling snow.”

2. **Visualisation of mathematical operations**

Possibly, many people – synesthetes and non-synesthetes alike – have some kind of mind's-eye visualisation on performing mental arithmetic. What they perceive and how they perceive it varies from person to person and might involve shapes, basic structures and spatial positioning. The more straightforward systems used by non-synesthetes as a habit to aid calculation, even if they automatically appear in the mind's-eye, wouldn't be considered synesthesia. However, for some synesthetes the numerical values have shape, colour, texture, spatial positioning and movement and a more complex automatic process takes place on solving maths problems. This could be considered a product of their synesthesia, or perhaps a way in which their synesthesia is useful, even if not considered a type of synesthesia in itself.

**These examples would probably not be considered synesthetic processes:**

"I simply see the numbers "stack" like tetris blocks."

"What's your thought process when solving 9+7? (...) 1 from the 7 gets tucked underneath it, that 1 gets slid under the table to 9, 9 uses it to build a 10, the remaining 6 jumps on top of the (10) table, & there we get 16."

(Source: this group conversation in the Facebook group Synesthesia. 2021.)

I physically see shapes combining with each other to form a stable shape like a square or rectangle. Also, sometimes when I add together numbers such as 7 and 8, I see the shape of the 7 hooking on to one of the holes of the 8. I was never taught to do addition this way, but I always understood that this was how it was done. (…) It happens involuntarily. (…) I don't see shapes when I look at individual numbers. It's only when I begin to add these numbers together that I begin to see shapes.

(Source: This post on the subReddit IAma: Ask Me Anything. 2011.)

**This account by a number synesthete involving shape, texture and colour suggests that the process has connections with their synesthesia:**

“This is how it feels like to add single digit numbers for me personally.

The numbers
on their own feel like different shapes, but if I am to visualise, let's say
"3+7" in my head, this is what it looks like.

All numbers
are sticks that get longer the higher they are, but they also have a
distinctive shape at the top, that matches with another number. And those two
numbers always add up to 10.

This
association is a lot stronger for odd numbers, the texture on the even numbers
is a lot less distinct.

2 and 8 are kind of like a Lego brick.

3 and 7 have a semicircle.

4 and 6 have half a hexagon sticking out.

And 5 is a diagonal that matches with itself.

I don't necessarily see the colours when adding numbers, but I decided to make them the colours those numbers have for me on their own.

Personally, I would describe the material these pillars are made out of as solid, but when two non-matching odd numbers combine, they kind of turn into a kinetic-sand-like material than then shifts and morphs until they fit?

I really struggled with going beyond 10 as a kid, since that is where this model breaks down. (…) Well not just beyond 10, but when an addition goes across a 10-boundary, you know? Like 27 + 6 is so weird to me. I have to visualise it as 27 + 3 + 3 so my brain can actually do anything with that.”

(Source: This post/comments on the Synesthesia subReddit.
2022.)

**Complex mathematical visualisations**

“Seeing mathematics”, that is, involuntarily and physically visualising highly complex mathematical operations with a tremendous amount of detail, is however a rare phenomenon. It might occur as a natural (developmental) type of synesthesia, although I am personally not aware of any cases. It appears to be more typical of cases of acquired synesthesia (or similar phenomenon) resulting from brain injury. This acquired type is the case of Jason Padgett, the man who “became a maths genius overnight” after being hit on the head during a violent mugging. (In this video, Jason Padgett gives an engaging, interesting and very recommendable TED Talk).

3. Moving on
to more common types, **number-form synesthesia** consists of perceiving
numbers as having specific and consistent spatial positions. The people who
have this type often benefit from it as they can mentally manipulate the
numbers they can “see” or even “touch”, finding them very easy to remember.

Go to the page on number-form synesthesia

4.
Synesthetes who have **grapheme-colour synesthesia with numbers** have a
particularly significant relationship with their digits when each one has its
own colour, and this can affect their mathematical abilities. Although some of
them have natural skills and great enthusiasm in this area thanks to their
synesthesia, for a lot of them it actually seems to create problems with maths
ability, giving rise to awkward situations such as “3 is yellow and 5 is blue,
but if you add them together they make 8, which should be green. But it’s
purple! I don’t understand, it’s wrong and it’s impossible for me to memorise
it!”

Go to the page on grapheme-colour synesthesia

5. For some grapheme-colour synesthetes, not only numbers and/or letters have colour but also mathematical symbols:

“Math
symbols have colors, too, like the root sign [√] is red.”

(Source:
the book *Synesthetes *by Sean Day (2016), p31. -You can get a pdf copy here.)

6. For some
people each number has a well-defined personality, so they also have a very
special relationship with numbers, seeing them almost as if they were people.
This is **ordinal linguistic personification** synesthesia. When they do
maths they sometimes have to deal with internal struggles between the
characters that affect them emotionally, although they also get the chance to
enjoy exhilarating stories of adventure, love, betrayal, vengeance or
solidarity, all produced by the dynamics of the digits and their interaction.
Obviously this can have an important effect on both their maths skills and
their concentration.

Go to the page on number personification

Go to the page on ordinal linguistic personification and personification in general

**This page last updated: 08 February 2023**

One thing I do experience is the idea that numbers have their own personality. However, it's not in a very anthropomorphic sense. Instead, a number like 17 is just 17. It's this prime number that has its own way of existing. I don't automatically know what a number's personality is; I have to get familiar with it. The 10 base system we use has an effect on how I see a number; specifically, it allows me to view it as an addition of powers of ten (duh). But as I get to know the number better, I think of its prime factors and stuff and that becomes central to its identity. I don't have a perfect memory; it's just a matter of how familiar I am with a number. I'm never going to forget that 111 is 3 times 37.

ReplyDeleteAll that being said, I consider numbers to have an intrinsic "personality" that I can become familiar with and this seems like a logical thing to do. That's probably not synesthesia, but are there any other opinions on this?

Numbers also have shape to them, but these shapes are not necessarily fixed, just like the personality. They are basically just polygons, so larger numbers aren't really that distinct, aside from the modular arithmetic you get, but I don't have all that memorized. I created this tool partly because I wanted to be able to look up the shapes of various interactions: https://cubicinfinity.com/modviz.html

For clarification, I don't only view numbers as polygons. The number 8, for example is easy to think of as the Earth cut into octants, as it is the simplest proper perfect cube (not the unit 1). 8 also makes me think of spiders :).

DeleteSometimes. Not all the time. My brain doesn't have time to think about spiders while doing math. 8 is too simple a number. But if I see 57, I'll often be like "Ah, 57. so common, yet so mysterious." but in a faster, less conscious way.

DeleteVery interesting comments. I love your modular visualiser, I will be having a go at that and see what it turns out! Maths synesthesia isn't my speciality at all, unfortunately, so I can't really point you in any useful direction. Numbers having personality is certainly considered synesthesia, but you're saying your ordinal linguistic personfication is of higher numbers too, any and all numbers, is that right? so it's different from the vast majority (where only single-digit numbers have personality and the bigger numbers are just combinations of those). But it seems quite logical to me that some people could have this, and it's perfectly logical that you would have to "get to know" the number before you realise what its personality is. It makes me think of Daniel Tammet's hundreds or thousands of numbers, each one with their own specific presence, shape, colour and so on, I can't remember if his numbers had personality exactly, but I believe they certainly had attitude! Anyhow you're probably familiar with the literature about him. I can't remember ever having come across or read about a case of anyone with separate personalities for all multiple digit numbers, but if I do I will reply to your comment here. I was thinking that Shereshevsky might have had separate personalities for all numbers but reading what he said I think he didn't: he just had them for numbers up to 9 and the two-digit ones would just be something like those two people meeting each other.

DeleteWhen you mentioned 111 thought of Oliver Sacks and the savant twins in the book The Man who Mistook his Wife for a Hat who had that instant concept of "one hundred and eleven-ness".

It would be interesting to know more about the personalities of your numbers. But I imagine they're a long way from the rather topical characters that ordinal linguistic personification seems to produce sometimes, and probably more about "attitude" and uniqueness.