Look at what Wikipedia says about the science behind mental exercise...

When mental exercise or stimulation occurs, specific actions in the brain take place as a result. Neurons connect with other neurons to form a network. Typically, people with more neural connections are expected to have a higher IQ than people with less neural connections.


Furthermore, mental exercise that involves using one’s non-dominant hand develops hand-brain coordination.^[2] A recent study has also shown that the brain is very similar to a muscle. This study says that during times the brain is being stimulated, it is actually growing in size, much like a muscle grows in size with exercise.^[3] 


When humans learn new things, the prefrontal cortex in the brain receives exercise. Also, the prefrontal cortex is the area of the brain that is known to weaken the most as age increases. This part of the brain controls reconciling contradictory thoughts, decision-making, foreseeing future events, and regulating social control. In addition, this area of the brain is strongly linked to a person’s general intelligence and personality. 


Therefore, it is imperative that the prefrontal cortex receives ample exercise to allow this part of the brain to remain sharp into old age. Without receiving enough exercise, it is possible that a person’s personality will change drastically during the later stages of life.^[4]