In my oughts and teens, I trained classical piano. Some days toward the end I was practicing for 4-6 hours during and after school, and I interviewed at the Boston conservatory. They told me they most likely would not accept me, but that's not really why I stopped. I knew I had to stop because despite over 15 years of serious intensive practice, I could still not make it through a 3 minute piece without my mind wandering off on some tangent of curiosity. At best my playing was distracted and unconvincing, and at worst (usual) I would screw up in the middle when my conscious attention came back to the present.
The only way I can stay task focused for longer than a few minutes at a time is by putting on headphones with a driving beat (EDM or similar) and stimulants. Caffeine is usually enough to get me through the workday. I'm a programmer now.
I made it through grade school and undergrad with respectable grades thanks to aptitude and quick learning, but I probably have an attention disorder that went undetected because of it.
>thinking and willing
One doesn't simply think away the structural defects in one's mind, any more than neurotypicals could transform themselves into genius IQs through force of will. A mind is shaped over time by internal and external influences, but plasticity drops off rapidly after the developmental years. Don't know your history of study, but why not browse through some videos of congenitally or traumatically brain-damaged individuals on youtube for some insight?