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I recently saw an episode of 60 Minutes about Jacob Barnett, a 13 year old boy who is currently attending advanced physics classes at a local university and was portrayed by the show as being a child prodigy/genius. In the interview, he demonstrates how he's able to perform mathematical transformations in his head by visualizing the numbers as colored shapes. As he explains in the linked clip:

This is 2 * 27: This is 2x27

He visualizes multiplying 2 by 27 as a series of colored triangles.

Is this a known phenomenon, and if so, does it have a name? Do other individuals visualize mathematics like this? Or is this just a 12-year old kid... embellishing (to be polite) his thought process?

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    $\begingroup$ As background context, there is a more general literature on the important role of visualisation in learning mathematics. A Google Scholar search for "visualisation in learning mathematics" yields many interesting articles including this and this. $\endgroup$ Jan 27, 2012 at 0:20
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    $\begingroup$ I can "see" some numbers as colors.. though It looks like the correct term is synesthesia, I've never heard of it.. $\endgroup$ Jan 27, 2012 at 16:11
  • $\begingroup$ Arent they all generally just called Savants? $\endgroup$
    – lightsong
    Apr 17, 2012 at 7:27
  • $\begingroup$ @abhiii5459 not really. "Savant" would be a good description of Jacob Barnett, but I was wondering if other individuals visualize mathematics like he described. They don't have to be savants. Also, the term "savant" isn't specific to visualizing numbers. $\endgroup$
    – Josh
    Apr 17, 2012 at 11:41

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Sounds like a form of Synesthesia, in particular it sounds like Number Form Synesthesia mixed with Grapheme-color Synesthesia:

A number form is a mental map of numbers, which automatically and involuntarily appears whenever someone who experiences number-forms thinks of numbers. Number forms were first documented and named by Francis Galton in "The Visions of Sane Persons". Later research has identified them as a type of synesthesia. In particular, it has been suggested that number-forms are a result of "cross-activation" between regions of the parietal lobe that are involved in numerical cognition and spatial cognition

It doesn't seem exactly like what he does but it could be a form of it. It's hard to imagine just how it would be to perceive the world as a synesthesic person does.

It sounds like he's learned to apply his visual-spatial skills to "arrange" the number forms to aid his calculations.

Synesthesia is covered in detail in the book Synesthesia: a union of the senses, though I'm not aware of any specific case studies on individuals with this exact set of skills.

A term to describe people with Synestesia is Synesthesic.

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    $\begingroup$ Wow, that's fascinating. It's also really interesting that you state It sounds like he's learned to apply his visual-spatial skills to "arrange" the number forms to aid his calculations because this occurred to me after hearing him explain. I thought, Hmm, this sounds like how a GPU can perform certain tasks much better than a CPU! $\endgroup$
    – Josh
    Jan 26, 2012 at 21:29
  • $\begingroup$ Reading Wikipedia further, it appears that Richard Feynman had Synesthesia. He may not have all the same skills as Jacob, but given that he was a Nobel prize winner, he was clearly a very intelligent man! $\endgroup$
    – Josh
    Jan 27, 2012 at 20:27

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