How to Better Approach New Concepts in Math or in Any Field

 You have, at your disposal, three mind faculties:

- Thought Initiator© - for thought inception and creation

- Thought Pusher© , or Referencer© - for manipulating thoughts

- Thought Visitor© - to visit established thoughts

With these faculties you manipulate thoughts in accordance to your wishes and motivations. Motivation is a mind state. Emotion is an idea. In order to effectively use these three faculties you consider everything as an idea or representations in brain, or mind. This includes complex structures like emotions, other ideas, objects, sensory inputs. Each of these have their representation in brain, mind and can be used to control them in order to take some actions or come up with new ideas. 

Many talk about awareness. This is often understood as some kind of meditation state. But there is more to it. In order to take full advantage of 'meditation' the awareness needs to be connected with these three faculties. With Thought Visitor© you visit various thoughts and state of minds (which are considered as a thought object, and idea) and see where they come from, when did you create them, and how they can be manipulated in your advantage. For instance, language is based on references. But, you form references using Thought Initiator© and Thought Pusher©. These are powerful tools of your mind and brain. A proof or demonstration of existence of Thought Initiator© can be the event when you send command to your nose to smell. This is Thought Initiator© ordering mind circuitry to smell. In the same way you can visit an idea, decipher from which axioms (postulates!) is derived from and manipulate it with your initiatives. Similarly, you identify two or more objects or concepts and using Thought Initiator© you form references and manipulate references or associations between these objects or concepts

With these tools at hand we can discuss how to better approach new concepts in math. Usually, how we learn math is by reading. We form references to concepts from words outlined in the text. But these words are borrowed from everyday life and often confuse us as we try to match their meaning with the referenced mathematical concept.

Instead of going following path from term to concept as shown in the picture, you need to follow path of the blue line. This means mask (hide!) the word used as reference and form an object thought from the side of theorems, definitions, and postulates that created or led to the math concept of interest. The math concept you want to understand has to be, as close as possible, explained and defined using set concepts, because almost all math concept, no matter how misleading are the terms that reference them can be explained by using set theory.

Digression: problem with education is that student has more difficulty to associate a reference word to referenced concept instead of focusing on referenced concept, how it is derived, what are the major postulates and how it is instantiated from its axiomatic system it belongs to.

As for other fields, other than math, the approach is similar. The term may need to be masked or replaced with your own reference, while the surrounding system needs to be defined from theorems, definitions, and postulates. Also, what is theorem in one system can be axiom or starting postulate in another. This is how you can creatively and effectively link systems from different fields like between math and biochemistry or biology and mechanical engineering. This method I developed for multidisciplinary teams I call Postulate Driven Implicative Truth Synthesis. More on this in my book, "Yes, You Can!".