The stresses that make body need brains and grow these brains and nervous system as a whole, are stresses that were encountered during evolution: hunger, need to endure (long walk, long work) and need to apply force (run fast, lift heavy).
When body experience these three stresses it produces brain derived neutrotrophic factor [1], which acts as a growth hormone for nervous system as a whole and also grows brain, in areas related to long term memory, higher cognitive functions (language, logic, spatial navigation, etc) and learning.
It works as if you can build "thinking muscles" which will help in every aspect of life.
E.g., if you barbell squat, you most probably will also run faster and you also will be more stable. Squats are not directly related to running, but they help nevertheless.
If you do endurange training and/or intermittent fasting, you will be more cognitively capable. Endurance training is not directly related to thinking, but it helps nevertheless.
So, yes.
An exercise for general purpose thinking is an exercise.
"Results: ...Groups of moderate (≈40) and high (≈49) fitness outperformed the group of low (≈31) fitness for inhibition and episodic recognition, whereas no significant differences between moderate and high fitness were observed (ANCOVAs). Breakpoints between benefits from VO2max for inhibition and recognition were estimated to ≈44/43 mL·kg−1·min−1 (multivariate broken line regressions)."
First, I think I should note that amateur boxing does not incur brain damage that is recognizable by contemporary methods. I see no studies contrary to that. Thus, basically, if you like boxing or other martial arts training, do that - having some exercise is better than not having any, and boxing is quite taxing.
Then, I should proceed to my main point: how martial arts training of someone's choice corresponds to the three stresses that elevate BDNF?
Typical martial art will train you for strength endurance. Strength endurance is an ability to exert about 30% of your 1RM for a prolonged period of time and training it is not directly a strength training neither it is an endurance training.
I think one should train for strength and/or stamina (direct relation with BDNF levels) and then take classes on martial arts technique (pattern recognition and reaction). This is how sambo/judo champions are trained, from what I know.
When body experience these three stresses it produces brain derived neutrotrophic factor [1], which acts as a growth hormone for nervous system as a whole and also grows brain, in areas related to long term memory, higher cognitive functions (language, logic, spatial navigation, etc) and learning.
[1] https://en.wikipedia.org/wiki/Brain-derived_neurotrophic_fac...
It works as if you can build "thinking muscles" which will help in every aspect of life.
E.g., if you barbell squat, you most probably will also run faster and you also will be more stable. Squats are not directly related to running, but they help nevertheless.
If you do endurange training and/or intermittent fasting, you will be more cognitively capable. Endurance training is not directly related to thinking, but it helps nevertheless.
So, yes.
An exercise for general purpose thinking is an exercise.