Interesting point, but there is a difference between being able to conceptualize mathematic principles, expressed in mathematical language, and motor skills, handled by the cerebellum in coordination with the motor cortex. The former ability allows a student to apply the principles to new situations, including practical applications such as engineering. The latter ability leads to a higher chance of getting a date with a cheerleader.
each new play is a new situation. “Math” has just two additional attributes:1) ability to communicate the thoughts to another person, 2) by putting on paper it allows one to proceed in a more logical path.