>>13137283Not necessarily so. Such reductions to abstraction don't work neuroscientifically in terms of just increasing specific intelligence. The brain is much more akin to a generalized pattern recognition system, wherein such neuronal clusters, neuronal networks, synaptic connections between such networks and clusters and the brain in aggregate have evolved for certain types of generalized pattern recognition.
What you could say, neuroscientifically is that, in some ways yes, doing certain types of intellectually stimulating forms of knowledge acquistion and application of such things, or "brain exercise" as you like to call it, will augment the capabilities of those parts of the brain and in general, the brain in aggregate as well.
It's important to think of this in the greater systemic context of what a morphological brain in aggregate is. This is a particularly interesting question to explore if for example, the corpus callosum is severed, connecting the two hemispheres of the brain.
A lot of the examples you provided, like mental arithmetics and playing chess, for example, are abstractly layered and compounded by the fact that they require many other forms of general intelligence to solve such a specific problem.
So to answer your question more succintly, it is variable on how you learn such things, with it being asymmetrically more inclusive of the particular task you are practicing, but not necessarily exclusive of other intellectual gains to be had.
It would be pretty fallacious to think for example, that some of the world's best chess players would not be somewhat good at math or logic, considering the fundamental basis of chess are math and logic. Maybe they're not as skilled as a mathematician or a logician in such things, but I bet they could compete quite well against such people, and in the same way, vice versa concerning mathematicians playing chess.