My 72 year old mother lives alone in a very isolated area, how can I convince her to move both for her mental health and personal safety?

I am assuming that you want her to move near you..yes? I was in your shoes exactly 3 years ago. It was so hard for me to convince Mom to move near us. Even though she had family in her little town, no one was really interested in checking up on her on a regular basis. When I finally arrived there to pick her up I was devastated by how pale and frail she was.
It also killed me that I was removing her from her home town and all that was familiar. But in the end I was doing what was best for her health and survival.
I would "plant the seed" now. Talk about how much you would love having her near you. Find a little apt. or assisted living center that is nice and send her pictures. Have her visit and stay for awhile...this way you both get a chance to see how things will work out.
One last piece of advice: please do not have her make this big move unless you are ready to take on the responsibility of caring for her. It was a bigger job than I had anticipated, but well worth it.
Good luck,
Lilli