Is the mathematician's activity psychologically healthy?
Well that looks like the behavior of any person with a strong passion and focus for his work. There are plenty of these around!

I guess it would be more common in any field of work were people already have dedicated a significant part of their life to it, and where it is almost a prerequisite. Being a mathematician selects and cultivates people able to display consistently that kind of behavior. Otherwise you just don't succesfully study high level maths, or fail at it. That is why you may observe many occurences of this phenomenon in your environment, when you work with other mathematicians.

Nothing to worry much about i think, there are plenty of people like you around, and this is not directly related to mathematics.