Three directions In this post:

This article proposes a writing framework to proceed with topological proof writing.

• The Formality.
• The Logic.
• The 'Ad-hoc' Tips.

I: Stay with the jargon and keep the formality in the earliest drafts.

This should be the first thing to keep from this post it would be the category title.

II: Keep the scores, keep track of the logic yourself.

By keeping the scores, I mean the references, and the logic in how you came to this conclusion, this will have the effect to improve your rigor and proof writing skills.

Writing a proof is about having less hand-wavy assumptions and using axioms or already proven theorems and corollaries for your work.

III: Then the rigor will come.

This is a framework I proceed with, I try to improve it and document it as long as I study in school. Will write more posts as well.

IV: BONUS: Don't shy from a failed proof.

If a proof turns out to be bad, learn from it, try to see why you think it would work out. This is what I do, I'd rather make 100 failed proofs on a conjecture than 100 successful conjectures proven (or disproven), I'd learn more from the first.