IMO understanding starts with writing in a clear as possible language.
Almost immediate followed with:
The following text describes certain concepts in use: There exists one Universe. This Universe exists now. We humans realize that we can define a concept called time. The universe is constantly changing. Every change defines an event. All events happening now, anywhere in the universe, are happening simultaneous. The universe is not empty, in the sense that it contains objects. Objects, like the unverse, exists now. The existance of each object defines a sequence of events.
To perform observations is a human conduct, which teaches us something, but performing these observations in principle should not interfer of what we are observing. That means the act of observations primarily raises questions which can be answered by performing more observations under different circumstances.
Observations also require certain specific tools. For example Galilea Galileo required a telescope to observe the planet Jupiter. But with Galileo his observations through his telescope was something special involved. What Galileo saw through his telescope, where not events happening now, but events happening in the past.
That means he saw the surface of Jupiter not the situation as it is now, but in an earlier epoch.
The important aspect of these tools is that you can do better observations with the emphasis that you do not want to disturb what you are observing.
In order to answer the question depents on what you want. Suppose you want to know how does it come that many stars have planets. Current observations reveal that this is the case. For more detail select these links:
It should be mentioned that performing experiments is the best way to learn about the evolution of physical processes using all different circumstances.
It can be used for almost all chemical, biological, mechanical, medical and physical processes. The most difficult are cosmological processes.
One important step in understanding a process is to start with a more simple case and to slowly make the process more complex.
Suppose you want to understand why can birds fly and secondly and what is involved for an airplane fly.
However a more philosophical issue is at stake: How important is mathematics in order to understand or explain astronomical, biological and chemical processes
All of this are physical processes. In general the answer is: not.
However if you want to understand the universe you must study the universe in its totality, as a complete chemical process, consisting of objects of all different sizes, which float in space, which influence each other but completely independent of human behaviour. What we humans observe is not the actual physical reality, neither are we capable to observe the physical reality.
For example, what we can observe, what is called length contraction. Length contraction can happen when observe the two ends of a straight rod. This involves two light signals, one from each end. Length contraction can happen when a rod moves "straight away" from an observer. In that case what the observer at each instant sees (simultaneous) are two lightsignals: one from the front and one from the back. The 'problem' is that these signals (events) are not generated simultaneous. The one from the front is generated earlier compared with the one from the back. The one from the front has to travel a longer path, this extra length is the length of the rod. All of that means what the observer sees is a shorter length than the actual length.
Something similar can happen when the rod moves straight towards us. In that case what we observe is length expansion.
When the speed of light is infinite and when the front of the rod reaches us, or touches us, at that same moment we also will observe the back of the rod. This implies that we see both ends of the rods simultaneous. That also means, we don't observe any length expansion.
When the speed of light is twice the speed of the rod the above is not true. When the front touches us, it takes a certain amount of time for a lightsignal from the back to reaches our eyes. That means the light signal from the front we observe comes from an earlier moment. This implies that the rod seems longer.
In order to understand the universe no mathematics is required except if you want to predict the future.
However there are more interesting issues to discuss. Understanding of the Universe involves chemical reactions which take place inside the objects. One type of reactions are collisions. The general rule is: What existed before the reaction (or collision) also exist after the reaction, but the type of elements involved can be different. A special type of reaction (or collision) where two atoms are involved or between an atom and an elementary particle. To investigate these reactions you have to perform them multiple times and observe what is created. In fact when you have performed identical reactions many times you know what you can expect (as the result of the reaction) and you also know in each case, if something is missing.
In some reactions what is created are electron's and the spin's are correclated. That means when one is detected as being in the +x direction, the other can be predicted in -x direction. And if this correlation can be established at a distance of 1 m or 100 m, there is nothing special involved. The simplest answer is that this correlation is established as part of the reaction. To claim that the correlation is established when the particles are measured is rather strange. The explanation is than that there exists some type of physical link between the two correlated (or entangled) particles and that is physical more incomprehanddeble).
A whole different subject is Uncertainty Principle. Does it make sense? As I already mentioned, all objects in the universe are influenced by all other objects; by forces. To understand the cause of these natural forces and to understand what the results of these natural phenomena is important and difficult. The question can than be raised how important is the uncertainty principle (With basically discusses human limitations, by performing measurements) within these issues. IMO zero. The problem is, in general, if a human being wants to measure any thing, the object or the state of the object is m odified. That means if someone wants two measure two parameters the errors increase.
When you want to simulate Newton's Law the original differential equations are replaced by difference equations. What that means, is that you start from the initial positions of all the objects in the universe at moment tn. That is the present position. You save these positions and you calculate the speed of all these objects. This requires also all the previous positions. Next you calculate the new positions of all objects and then these become the present positions. (more or less)
The point is that the universe also evolves more or less in this way, but not so much discontinuous or step wise, but more in a continuous way. That means the present positions of the whole of the universe physically changes continuously
How ever there is one basic problem: Objects (events) influence nearby objects almost immediatly, but for events at large distances of certain objects, to influence these far away objects, takes time. The best way is to study a binary system. Each object is not influenced by the present position of the other object, but by its position in the past. Newton did not include this propagation issue.
STR and GTR introduced a whole new approach. One main problem is that STR uses a clock while Newton's mechanics more or less assumed that the time in his universe, which was more or less the solar system, was based on one central/universal clock. Remember that resembles very much the physical world operates: there is no physical clock. The solar system is stable by itself.
The problem starts as soon when you start to introduce physical clocks, because allmost by definition all the physical clocks run different and are influenced by all type of forces. Synchronisation of these clocks is also a difficult physical issue.
But there are more issues. In Newton's mechanics there is generally speaking no, or only one observer. In GTR almost every object becomes an observer, being at rest within its own reference frame.