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Josh
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Have any studies been done on individuals who can "visualize" numbers and advanced mathematics?

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?

Josh
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