How to think about Maths without dying in the attempt?
If it hasn't been said enough, or in most cases this seems to be ignored—whether deliberately or not—by educational institutions, it is largely due to how we understand and construct mathematics from within the issue. Educational institutions, whether private or public, tend to or are unable to teach mathematics as a language, just like any other language that is intended to be taught.
Mathematics are essentially a linguistic invention of human beings to understand ideas or their immediate environment, and at the same time abstract concepts outside of tangible reality that only find a place within systematic explanations.
The idea of mathematics is symbolic and ontological, a branch of first philosophy that studies "being, existence, and reality" - things that mathematics seeks to prove. But I don't want to overwhelm the reader with so much boasting about terms if the goal is to understand mathematics better.
Like any language, mathematics has structures in its relationships. In other words: no concept exists without another concept. Within academic institutions, I often see that each topic is taught as a standalone concept, with the simple explanation "it's because it is," without really motivating the student to understand what leads to that concept working in such a way. Each mathematical concept, being a piece of reality, which the human observes to later propose some conjectures in order (logical) to explain the phenomenon. These are elaborated as theories and laws, which start from other conjectures (made previously theories and laws), to explain themselves as a system. Each system is integrated as a word into a language, and that language is mathematics.
At the same time, mathematics is tireless and infinite, where as infinite beings that we are, we must constantly reinvent them, make them expand and address new concepts (such as the process I described earlier) that are more refined and more precise for various areas.
If we stop thinking of mathematics as rigid dogmas, without flexibility, separate from each other, and that "they are because they are", we will possibly leave the lethargy of mathematical interest aside.
Let's not think about the numbers or letters that seem too complicated or strange at first glance, but rather, what do they want to communicate to us? One must have a trained abstract thought, for this, philosophy and one's own doubts can be useful. When we exhaust all the speculative capabilities of philosophy as only human reasoning and our "reason" is no longer sufficient, it is preferable to start working together with mathematics. There are some mathematical concepts that initially seem strange and unintuitive to our level of reasoning, but through various systems, as if they were sentences, they seem to take a new path and make sense of themselves.
When mathematical thinking is developed and practiced, the rest of human languages (which also rely on symbolism and mathematics) become easier, allowing one to more easily identify structural problems (even very slight ones) at a glance. Understanding mathematics involves not only knowing how to solve quantitative problems, but also eagerly engaging in diverse readings that always encourage critical thinking about things; mathematics is a fertile foundation for more solid argumentation in the field of social sciences. In addition to improving mental acuity.
Another issue in this regard is the fear that mathematics causes us when we first encounter it. A teacher who decides to teach them as dogma knows just as much or less than you. The main reason for my previous statement is one thing: you are ignorant of the concept because it is the first time you have entered the subject, the professor is more ignorant because he has been in contact with the subject in depth and still refuses to teach it from the reflection of the concepts, that inability to teach and believe in understanding the concept, clashes with the innocence of the student who, when asking questions about its operation, the professor is not qualified to answer, because they would have to explain the system itself, and not its symbolic production on a sheet of paper.
The least important aspect of mathematics is the resolution of things in writing, but rather the human attempt to reflect and play with concepts to create new words or theories. Changing the syntax of mathematics without losing cohesion, that is the true beauty of mathematics. I think that, for a deeper interest in mathematics, what I would least do is present a book on algebra or geometry, but rather a book on mathematical thought in words.
