Is the mathematician's activity psychologically healthy? I am a professional mathematician, and I regularly meet other mathematicians.
I have come to wonder if there is something like a slight neurosis, specific to this activity.  

To be more precise, let me grossly describe the mathematician's activity:
The mathematician tries to solve a problem. This problem is usually sufficiently hard to not be solvable without an intense concentration. There are two types of concentration here:  


A local type: the intensity in the moment (i.e., all the thoughts are focused on this single problem).  
A global type: the commitment in time (i.e., work on this problem for months, even years).  


Usually, the local concentration can be sufficiently intense so that the mathematician loses the feeling of hunger, thirst or sleep. In this state, there is usually no room for a healthy relationship with others.
It is almost as if the mathematician has a state near that of autism (see Asperger syndrome).

The global concentration permits one to develop in the time a more and more intense concentration on the problem. The mathematician is committed "body and soul" into solving the problem and could neglect all other aspects of his life like social relationships, married life, children...
It is almost as if the mathematician has become more and more autistic.  

So ok, autism is a severe neurosis and it's usually irreversible. It's the reason why I speak about a slight neurosis specific to mathematicians, because it's usually reversible...     

In light of what I wrote:  


  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.