Even World # 1 (my previous post, How to Easy Understand the Role of Mathematics in Physics, Economics, and Other Fields ,) has to have its own axiomatic systems and what you can do inside the world. Obviously, this set of axioms in World # 1 will dictate which axiomatics realizations we will have in the World # 2 (example, World # 1 are vectors and vector operations, and World # 2 is math, or World # 1 is physics, and World # 2 is mathematics). Confusingly, for instance, sometimes, the sub domain of mathematics of interest is called vector's mathematics, but there is no such thing. There is only a part of math constructs that are triggered or motivated by vectors. Vectors itself ARE NOT mathematics. They are spatial, arbitrary constructs, concerning length, direction, that happen to interest us. They also came out of the blue.

The confusion arises with rapid and continuous jumps between World # 1 and World # 2, so one can get a sense that math is so intrinsically connected with World # 1 that without it a specific formula would not exist. That's not true. Formula would exist in mathematics in any case, but what the numbers represent, i.e. what they are counts of, must be explained in World # 1.

More on math:

The confusion arises with rapid and continuous jumps between World # 1 and World # 2, so one can get a sense that math is so intrinsically connected with World # 1 that without it a specific formula would not exist. That's not true. Formula would exist in mathematics in any case, but what the numbers represent, i.e. what they are counts of, must be explained in World # 1.

More on math:

- Real world examples for rational numbers, for kids
- Math and its relationship with real world
- How math can be applied to so many different fields?
- Where the graphs in mathematics and physics come from?
- Tweets about math, physics, and how to approach math calculations
- One insight about mathematical axioms, logic and their relation to other disciplines
- How the ideas are born and notes on creative thinking
- Mathematics Axiomatic Frontier
- Why math can be an independent discipline?
- More on creative thinking, math, innovations, physics, emotions
- Comparison between making movies and math and physics
- More tweets about math
- Domains of math applications and math development
- Where all those number series in math are coming from?
- How to understand the role of math in economics, physics, engineering, and in other fields