One more thing: In all this, mathematics is totally neutral. People often confuse "mathematical models" (sothing that a natural scientist does) with mathematics (which mathematicians do). Mathematics is not concerned with "truth" at all. All math theorems say "if A than B", but they NEVER tell you whether A is true or not. Math creates pre-fabricated logic containers, it is not concerned with the truth values of their "inputs".

Hence, you should re-formualate your question as "Do mathematical models present solutions for understanding the reality of the universe?". The answer is then obvious: some do, some don't. And often several model lead to the same conclusion. That's all, folks :-)

Farhad Vedad , I think that you fall a bit prey to the tendency to oversimplify history. It is true that the Jesuit Christopher Clavius, the father of the Gregorian calendar, was initially a staunch defensor of the geocentric system, but it is also true that he was a scientist who did not ignore other hypotheses and studied them assiduously. He and Galileo knew each other well, and respected each other mutually very much. In his later life Clavius accepted most of Galileo's teachings. The Catholic church of that time was much less ignorant than what is generally taught in schools today. Their objection to Galileo did not regard so much the substance of his teachings - they knew perfectly well that he was right - they objected to his "breaking out the news to the public" so fast and in such a vehement way he did. It was disrupting public order! That was the only reason why he had to recant PUBLICLY (not "just" recant - nobody really cared about that) and also the reason why he was subsequently given such a light sentence (his villa in Arcetry with its surrounding estate was a very pleasant place where to live and receive frequent visitors). Sincerely, the Gregeorian (pardon, Clavius') calendar is such a mathematical-physics jewel that suspecting Clavius of being narrow minded would be really unjust. It will serve us well for many millennia without any retouches than those already planned.

This said, I understand where are you pointing in your last paragraph, and I sympathise with it. Just do not forget that apparently different models of reality can indeed lead to identical practical results, or ones that differ less than experimental uncertainties. This leaves the models (theories) in doubt, but actually reinforces our trust in the results, don't you think?

One more thing: In all this, mathematics is totally neutral. People often confuse "mathematical models" (sothing that a natural scientist does) with mathematics (which mathematicians do). Mathematics is not concerned with "truth" at all. All math theorems say "if A than B", but they NEVER tell you whether A is true or not. Math creates pre-fabricated logic containers, it is not concerned with the truth values of their "inputs".

Hence, you should re-formualate your question as "Do mathematical models present solutions for understanding the reality of the universe?". The answer is then obvious: some do, some don't. And often several model lead to the same conclusion. That's all, folks :-)

I think the following article says more about the relation between mathematics and sciences

https://booksc.xyz/book/1211813/354364

The unreasonable effectiveness of mathematics in the natural sciences. Richard courant lecture in mathematical sciences delivered at New York University, May 11, 1959

Eugene P. Wigner

It helps if the fundamental physical laws are laid in mathematics: conservation, change, transfer and packaging of energy.

A profoundly philosophical question - outside my remit I'm afraid

I agree with Prof. Stan Sykoyra. Mathematiics is just a tool. It giveaway only solution fo an equation . For example, Turing theory of Chemical basis of morphogenisis postulates second order differential equations. It gives satisfactory results for certain patterns but not all patterns. So the Model was to be refined and it was done as next step.. There are similar examples. Einstein theory us an other example.

Stan Sykora Dear Stan, I really liked your suggestion to change the question to "Do mathematical models present solutions for understanding the reality of the universe?"

However, you knew what I meant.

If we assume the space homogeneous and also assume that the speed of light in vacuum is constant due to constant refractive index and then we assume that particles may behave such as wave conditionally, or in opposite way, we assume that the space gets homogeneous when an object is being located in, and subsequently the refractive index of the space gets non-constant and we assume that particles including the photon moves as a particle then in both assumption we may use the same mathematical solution. Now, SSUN in this assumption rotates around the EEARTH or vice versa?

Dear Farhad Vedad . If you create a model containing lots of pretty arbitrary assumptions and then construct a question that cannot be answered in that model, the only thing I can say is "so what?". Another possible answer is "does it matter what rotates arout what"? As long as some measurable quantities can be correctly predicted by the the model, it may well be useful. It is likely that no model human-build model will ever explain everything, which is beautiful and soothing. Would you like to live in a totally predictable Universe? Me not.

Stan Sykora Dear Stan,

I raised this question because of the result of some of my experimental works. They show that light speeds down while passing nearby the surface of an object and consequently when it passes through a slit or a pin whole. The wave-particle concept may not explain this since the speed of light has been assumed consistent in that concept. From the other side, if my experimental works are true, then the only assumption left is that the refractive index of the space may not constant and so on to what I mentioned before.

"Invention will follow invention. The unexpected is often a valuable clue." - Alfred P. Morgan, introduction to The Boy Electrician, 1947

I have run into many situations in my life similar to the one you describe above. In all cases, it was not current theory that was the problem, but my understanding of the problem itself. Once I knew the result, it was relatively straightforward, although not always easy, to work backwards mathematically to determine the cause. That said, many breakthroughs are found through anomalous results. Just as often, anomalies accumulate until a theory comes along which explains them. The "ultraviolet catastrophe" and the existence of ether are a couple of old examples. The existence of dark matter and energy are a couple of new ones. In all cases, mathematics are simply a tool, as mentioned above, used to describe reality to better or worse degrees of accuracy. If the math doesn't work, you usually need better math or a better theory. Reality tends to be an unrelenting taskmaster.

Mathematics is simply a language for communication, one among many.It does not of itself supply "understanding", "truth" or "reality". It is however a special language, one that has some qualities of universality, beauty and which can occasionally lead to unique insights.Mathematicians or would-be mathematicians tend to rate its usefulness very highly, while it has no bearing on the lives of the vast majority who treat it as background noise.