I read a while ago a science fiction story about becoming immortal.
The story starts with a couple on a generation ship, when they receive a message from Earth about a cure for mortality. The wife and son then choose the cure while the husband and daughter don't.
The story then goes from there to progressively describing the evolution of the wife and son. They first become robots, then energy beings.
Other details of the story include the wife rejecting the son when he becomes a robot, the wife watching a black hole for a few million years, etc.
The ending of the story has the wife create some new intelligent life on an alien planet. I had thought that Ted Chiang wrote this story but apparently not.