Definition. Becoming aware of corner conditions only by experiencing them is called ‘the school of hard knocks’.
Children who haven’t even mastered long division are supposed to do scientific research?
Scholarship is intellectual labor that is at least, say, 80% enabling (e.g., dictionary-creation). It is possible to do intellectually heroic work (such as a detective who solves a difficult case) without being a scholar.
It is what you have written that goes with ease onto the blackboard, not what you have seen.
Mamikon’s Theorem is the greatest advance in Calculus since the time of Newton. His theorem is the basis of what has become the discipline of Visual Calculus.