It depend of your definition of problem :
A problem is an obstacle, impediment, difficulty or challenge, or any situation that invites resolution; the resolution of which is recognized as a solution or contribution toward a known purpose or goal. A problem implies a desired outcome coupled with an apparent deficiency, doubt or inconsistency that prevents the outcome from taking place.
1. any question or matter involving doubt, uncertainty, or difficulty.
2. a question proposed for solution or discussion.
3. Mathematics. a statement requiring a solution, usually by means of a mathematical operation or geometric construction.
So, if you definition is more in the line of Wikipedia, no we don't really solve any problem. But if you take it in the line of dictionary.reference, we solve some. Those problems are less practical than, say Stackoverflow, cooking or home improvement. They are also less useful since they are about imaginary universes. But they are still problems.
Peoples are puzzled by all the information that is available about Sci-Fi and Fantasy. Accessing, filtering and extracting the meaningful information is the real problem, that's why we are here.