we don’t have a step-by-step checklist to follow in order to use informal mathematical arguments
If we did, the checklist would define a form and the mathematical arguments would become formal.
Terrence Tao uses the term post-rigorous to describe the sort of argument you’re talking about. It’s one of three stages. In the pre-rigorous stage, concepts are fuzzy and expressed inexactly. In the rigorous stage, concepts are precisely defined in a formal manner. In the post-rigorous stage, concepts are expressed in a fuzzy and inexact way for the sake of efficiency by people who understand them on a rigorous level; key details can be expressed as rigorously as necessary but the irrelevant details of a full proof are omitted.
we don’t have a step-by-step checklist to follow in order to use informal mathematical arguments
If we did, the checklist would define a form and the mathematical arguments would become formal.
Terrence Tao uses the term post-rigorous to describe the sort of argument you’re talking about. It’s one of three stages. In the pre-rigorous stage, concepts are fuzzy and expressed inexactly. In the rigorous stage, concepts are precisely defined in a formal manner. In the post-rigorous stage, concepts are expressed in a fuzzy and inexact way for the sake of efficiency by people who understand them on a rigorous level; key details can be expressed as rigorously as necessary but the irrelevant details of a full proof are omitted.