Definition of rigor I always seem to get downvoted when my answer is not "rigorous" enough. I have started to get a feel for this "rigor." There should be a proof element, nothing can be assumed, and the proof should be near purely mathematical and rigid. My english teacher even got mad at me for using "rigor" incorrectly today, so that reminded me of this site. What defines mathematical rigor?

A _rigorous_ argument requires _precision_ and _proof_ , where the proof relies on a set of theorems ultimately leading to a set of stated axioms. If an argument is rigorous, then the steps in the solution should be unambiguous such that anyone else could reach the same conclusion with the steps.

Your interpretation is fine in a mathematical setting. An english professor might not understand the nuances of mathematical rigor.