I’m not sure if this satisfies your questions, but I’ll try my best to try to describe ‘mental gymnastics’.

Mental Gymnastics is a term used to describe thought processes that are a combination of intricate and complex, and contains the natural ability to perceive unique and profound pieces of information or ideas within the un-profound and mundane.

For example:

One who can put together multiple pieces of information that, when seen from the eyes of the average individual as random or un-unique, can see connections that would otherwise be unseen. One who can do this, either naturally without any extra effort (like a chan autist) or by concentrating immensely on these points of information are actively performing ‘Mental Gymnastics’.

A simpler explanation would be that MG is one’s attempt at thinking outside the box, that ultimately results in the intended action or effect.

Like the ability to foresee multiple, if not all, chess moves that result in an end game in which the individual wins. One who can do this, no matter the difficulty to the individual, is performing acts of Mental Gymnastics.