Let us begin.
The common denominator in any equation is always relevant to the question/problem. The solving of which always depends on the expertise of the process (or knowledge) by the one working out the equation. e.g. A first grader has no understanding of trigonometry since he/she has not yet learned even the basics of simple arithmetic.
Everything it seems is based on previous information, having been built up in levels over time.
Each new facet of the gem is cut, ground and polished according to the expertise of the craftsman doing the work and is valued accordingly. The quality is enhanced or diminished by that expertise or the lack of it.
Training is important in developing skill and logic, but it takes more than training to create a Master.