The 4 pillars of math that I stand by

Over the course of several years of learning math, I have converged on some theories that I feel that I should call it by the pillars of math. Different people have different theories so here I present mine. It is difficult always keep this theory constantly in my mind so I will try my best to remember them. (I always have an idea that it is the 4 pillars of math)

1. Observation
   At the beginning of math, people observe the nature and use their current knowledge to explain the phenomenon that is around us. Several concepts arise from the observation. From looking at fly at the edge of the room give rise to the graph using x and y axis we know today to the wonderland we know of today. You can see what I mean from this book

2. Abstraction
   This pillars tries use one explanation to fit all possible scenario. The concept of algebra, the concept of infinity and through the power of the pillar of observation, formulas and laws of physics has been created as a result. These idea explains a certain concept regardless of the situation, yet the formula remains unchallenged. Even as new discoveries are made, they remain unaltered, consolidating all possible permutations and scenarios and arrive at a conclusion. Ypu can look at the power of infinity at the book here.

3. Extension
   This involves people using their imagination to create theories that extend beyond what is physically possible. The important feature is that the extension should not cause any contradiction to the concept we know of today otherwise we need to rethink of how we understand math. Theories that extends beyond 3 dimensional vectors, number system that go into the complex domain to quaternions. The list goes on. Yet the properties are still consistent with the theories known before.

4. Language
   Math inherently has its own language. It has vocabulary which allows people to express different operations. It also has it own grammar otherwise known as syntax. Within each area of study, there is a syntax and system that is expressed from the language of mathematics that corresponds to the other 3 pillars. New operations and type of numbers will probably be discovered that will transform the math that we know today.