/sci/ - Science & Math

Why is Mathematical Reasoning not a separate field from Mathematics in general? Mathematical reasoning has more to do with psychology and requires the development of mental skills and an evident progression linking one concept to another, rather than the common approach of maths that's focused on proving and memorizing.

Currently maths is like managing a library, it organizes a vast list of facts to be consulted, but other than consulting an index and taking for granted what is found, people in general are not able to wield it. Those who are capable of it have developed their math reasoning without help, which is an extremely inefficient way of acquiring the skill, and the reason most people have anxiety towards math.

So why has nobody taken the approach to organize math with focus on the different ways to visualize a problem, the different ways to reach a solution and taking notice which procedure is the most intuitive for that?