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I have personally never been able to do that! by saying "study" I don't mean doing "home work" or reading a book; I mean research. for example:

  1. trying to solve a difficult mathematical problem in the morning.
  2. composing music in that afternoon.
  3. writing story during the evening.

this is a bit funny but Leonardo da Vinci had done it before(the example I have given is not from his history)! This make me wonder if its really possible?

I have seen people who talk while solving a math problem, but I am not talking about people who solve problems in habit. I am talking about mathematical ideas where each new idea is different from others and need special attention every time. I believe that this type of problem solving ability cannot be made faster or habitual with attempts to solve various problems. Again: I am not talking about math homework.

UPDATE:

my question is will diverting one's mind in vast fields of art rigorously affect his mental health or is it actually possible? If there had been a Newton there had also been an Einstein, Faraday; if there had been Beethoven there had always been a Mozart. Its obvious that Leonardo da Vinci had been an expert in more than one subject; but who else have been like him? No one! So is it practically possible to learn more than one subjects?

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Different areas of the brain can be active simultaneously. People who regularly do maths (research job etc.) can typically have a conversation while computing the maths. –  FraserOfSmeg Jun 24 at 10:35
    
I think that all those people that did it before, had practice. It sounds like something that needs time developing. I assume that some scientists lived like that. But they invested a lot of time in it. It doesn't sound impossible at all. You don't know if you don't try. Tho, I don't believe there is any research on it, because it's individual thing,also hard to measure. What metrics would you use to prove it,it is possible? Amount of science papers, music sheets and book published in a year? Also,everything can become a habit over time and to solve such problems,u need some serious habits. –  JunJun Jun 24 at 14:36
    
It's not clear to me what you are asking. Clearly people can learn or work on multiple things over the course of a day, but I don't think that's what your question is about. –  Josh Jun 24 at 15:14
    
my question is will diverting one's mind in vast fields of art rigorously affect his mental health or is it actually possible? If there had been a Newton there had also been an Einstein, Faraday; if there had been Beethoven there had always been a Mozart. Its obvious that Leonardo da Vinci had been an expert in more than one subject; but who else have been like him? No one! So is it practically possible to learn more than one subjects? –  user3633270 Jun 25 at 17:12