I love the clarity of Math, where something is, or not, with few grey areas Life is not like that, and a story is a description of life, even if it's an imaginary life on a fictional world. Usually there are no straight paths, rather a network of roads, avenues and trails that we negotiate the best we can, never being able to see, much less explore, all the possibilities.
I'm by no means an experienced writer, but to me having a good idea on how the story will end is essential. Without it I'm lost.
I also draw a "road map" with the relevant "places" where the story should pass, but my map is like the medieval ones: Everything is out of proportion, legends fill the empty spaces and there are imaginary places that I never find.
Anyway all writers (AFAIK) tend to agree that experience is fundamental. The more you write the better you do it.
So let's do it!
Yes to all the things! Especially the first paragraph. Your maps sound pretty fun, I might try that method of planning.
*cough* Gödel's theorems, P =? NP, Continuum Hypothesis, ...
I don’t think of Gödel’s incompleteness theorems as something fundamentally fuzzy. Because if something is unprovable (in some system!) then the fact "the something is unprovable in that system" may still be provable in some other system. It reminds me more of the things we can’t calculate or the things we can’t construct (in finite time). An example is
Goodstein’s theorem, which is unprovable in Peano Arithmetic, but provable in others. It has nice visualisation/application with Hydras (
this video explains stuff a little & might be interesting, but I haven’t watched it fully).
And although math is pretty "clear" and "simple" in some sense – only rarely you have to juggle ten concepts at the same time – this doesn’t imply for me, that all questions have to be answered already. There will probably always remain interesting open problems.
So I only consider your mentioning of the continuum hypothesis to be something of a grey area. It differs a lot in tone from the others, since the question now (after having proved its independence of ZFC) is: "do you want the continuum hypothesis or not in your set theory?". And there are many "questions" like that (large cardinals, axiom of choice, intuitionistic logic, alternative foundations, ...), which aren’t questions about a thing, but a choice with what you want to work with. It *might* just happen, that these things interest me.