Musician does not spend 8 hours a day playing music at work and then plays at home in addition to it. Playing music at home is not addition to full time work.
Same with mathematician, actually. I know, because I have them in my family. They do math for work, whether at work or at home. And they do have non-math hobbies.
Writer is not writing 8-5 in work just to come home for hobby writing. Writer either writes for job or has non-writing job.
> A chef might have an idea for a meal and experiment at home.
100% not. Chefs work long hours and when they come home, they want partner to cook.