In modern computers (and programming) one makes alienated use of the high powers of graphical processing units (GPU) for non-graphics-related tasks, enhancing drastically the power of the general purpose central processing units (CPU).

I wonder if any attempts have been made to explain high-performance in abstract (but geometry related) mathematics (by people like William Thurston, Sergej Perelman, Alexander Grothendieck, to name just a few in no specific order) by an extraordinally strong and specific use of the visual cortex (and not only of the associative, speech-related and other parts of the cortex that are usually involved in mathematical thinking). At least the role of "inner geometric visualization" is often emphasized (without being completely understood, as I guess - not even what this means).

For example, in his laudation for the Fields medal winner of 1982, William Thurston, C.T.C. Wall says:

Thurston has fantastic geometric insight and vision; his ideas have completely revolutionized the study of topology in 2 and 3 dimensions, and brought about a new and fruitful interplay between analysis, topology and geometry.

So my question is for any study that might have been performed in this direction - or for any theoretical approach that has been made.

[One guiding idea might be the following: Consider the concept of a 5-dimensional hypercube. Just trying hard and often to mentally visualize such a cube (which would correspond to some specific neuronal activities in the visual cortex) would "improve" (somehow) mathematical thinking about higher dimensions in other parts of the cortex - even if it's not successfull, i.e. no clear mental picture arises. (Of course, trying to do so would be "informed" by those other parts, so dependency is bidirectional.)]

Possible follow-up question (not to be answered here!):

Which characteristics of either the visual cortex or the other parts of the cortex being concerned with mathematical thinking make it possible to use the visual cortex in this way (whatever "this way" is)? Or could just everyone use it this way?


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