Hypothesis, axioms and models
One should not think that everything can be proved with physics and mathematics. All physics, and also mathematics, is based on assumptions, each of which is variously called a hypothesis or axiom or postulate, etc.
For example, the universal law of gravitation proposed by Newton is an assumption or hypothesis, which he proposed out of his ingenuity. Before him, there were several observations, experiments and data, on the motion of planets around the sun, motion of the moon around the earth, pendulums, bodies falling towards the earth etc. Each of these required a separate explanation, which was more or less qualitative. What the universal law of gravitation says is that, if we assume that any two bodies in the universe attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them, then we can explain all these observations in one stroke. It not only explains these phenomena, it also allows us to predict the results of future experiments.
A hypothesis is a supposition without assuming that it is true. It would not be fair to ask anvbodv to prove the universal law of gravitation, because it cannot be proved. It can be verified and substantiated by experiments and observations.
An axiom is a self-evident truth while a model is a theory proposed to explain observed phenomena. But you need not worry at this stage about the nuances in using these words. For example, next year you will learn about Bohr’s model of hydrogen atom, in which Bohr assumed that an electron in the hydrogen atom follows certain rules (postutates). Why did he do that? There was a large amount of spectroscopic data before him which no other theory could explain. So Bohr said that if we assume that an atom behaves in such a manner, we can explain all these things at once.
Einstein’s special theory of relativity is also based on two postulates, the constancy of the speed of electromagnetic radiation and the validity of physical laws in all inerlial frame of reference. II would not be wise to ask somebody lo prove that the speed of light in vacuum is constant, independent of the source or observer.
In mathematics too, we need axioms and hypotheses at every stage. Euclid’s statement that parallel lines never meet, is a hypothesis. This means that if we assume this statement, we can explain several properties of straight lines and two or three dimensional figures made out of them. But if you don’t assume it, vou are free lo use a different axiom and gel a new geometry, as has indeed happened in the past few centuries and decades.