And remember, even Hardy, most famous of the Purists, often slummed it with (hold your nose) physicists and on a few occasions even with (the horror) biologists.
There are quite a few female mathematicians who made important contributions. My wife wrote a top 10 of sort on my blog a few years ago: http://math-blog.com/2008/09/28/10-remarkable-female-mathema...
If you spend all day thinking about others, you won't get any math done. If you spend all day thinking about math, you won't be in tune with others. If you can balance things out properly, you can do both.
Sometimes it's necessary to go to one extreme for a long period of time. If you're working on a really hard problem, it might be best to isolate yourself from society for days/weeks/months at a time to figure it out. If a close family member is stricken with a major illness like cancer, it might be best to focus and spend your thoughts, time, and emotions entirely with them.
In reality it's usually a balancing act between different things. But you can understand why it's sometimes necessary to go to extremes.
But we can't forget that there are huge brain changes when you are young.
Businessmen can delegate and use the system set up in their young adult years to continue their trajectory. Franchising is an example that comes to mind.
I have always admired Paul Erdős, a really interesting life doing something he loved.