One important consideration when you want to do science or physics etc, all the concepts used should be clearly defined.
One of almost the first subjects to discuss is the role of mathematics in physical science.
My own understanding if you want to do science, that means if you want to understand the evolution of the physical processes in the universe you don't need mathematics. The reason is that the evolution of the universe involves all different types of physical processes i.e. gravitational, chemical, electrical, magnetic, mechanical and biological processes which all are based on physical products which change and interfere which each other in the course of time.
That leads to the conclusion that the understanding is similar. That also leads to the conclusion that the way how processes interfere within each and between each other follows similar lines.
One type of systems that can be studied are mathematical systems. These systems don't exist and operate and are described in mathematical space or frame.
What also can be said that physical systems are described in physical space or a physical frame.
In Mathematical space we can speak of lines and points. In physical space lines and points don't exist, only 3D objects. This sometimes leads to wrong conclusions. For example: in physical space the distance between two objects (calculated from the centre of these objects) can never be zero. This leads two the wrong conclusion in case of Newton's law (division by zero).
That does not mean that in physics no mathematics and equations can be used. Mathematics used can be tricky because it is based on accurate measurements.
To perform science you must start with a certain world view. This world view describes the bassic concepts about the evolution of the universe.
Such a world view gives a certain common starting point to describe the universe in all its details and complexity.
For me the starting point should be that at any moment during the evolution of the universe we define a now (also called universal time). In the universe there exist objects (small and large) i.e. atoms and molecules and the rest is physical space. From a human perspective we can call physical space empty, but from a physical point this is not true, because it contains photons and fields. It should be understood that in whole of the universe there are gravitational fields, implying that the universe is not empty.
At each now all the objects atoms and molecules in the Universe have a certain position. All these positions also identify events, which all happen simultaneous.
You can also consider one specific object and define its position as a sequence of equally spaced events. All these points define the trajectory of the object through space.