Just finished The Three-Body Problem trilogy. What a saga. I finished the last book a month or two back and I still find myself randomly thinking about various ideas that I picked up in those books. If you're "serious" about sci-fi, I would say that you really do have to read those books as part of your "curriculum".
My mom loves sci-fy, but she probably doesn't have the math/physics chops to hit something too deep in those topics.