I do not want to generalize but physics is not an equivalent of physical world Some Maths models work in Physics but it does not mean that they cover all phenomena in the physical world Its the task of science to describe things around us with most precision Im sure Physics have been utilizing Mathematical means successfully thus far Am I right?

Dear Ruslan Pozinkevych;

Yes, that's largely true, but it seems like the days of more exciting work in physics are over!

Seyed Mohammad Mousavi

An excellent question, Seyed, because many folks look at mathematics for all the good things it presents us, but then accept it as if the gospel got pronounced via mathematics.

The most important truth about mathematics is that it is an abstraction by itself. We do not have a drink with 'Three' in the bar, or take 'Eight' for a walk in the park.

1 + 1 = 2 does not mean anything by itself, we need to turn that into 1 apple + 1 apple = 2 apples to finally have some contents to the abstract eqation.

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The abstraction that mathematics presents us will mostly be about reality, but the abstraction can be about an artificial reality, too.

Allow me to work this out in simple terms.

Reality shows us that we can apply mathematics to it. And yet part of reality are artificial aspects, such as paintings, television screens, and the likes. So there is a 3D reality and there is a 2D reality, and mathematics can be applied in both realities.

Other examples of artificial realities that we appreciate very much in our true reality and may not consider abstracts by themselves are money, language, and let's add religion to this list as well.

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An important example to make the fine point clearer is found with the term infinity.

Almost everyone understands what is meant with the term, yet there is actually extremely little in real life that is infinite.

• The one 'item' I can think of that is infinite indeed is Space.

Some argue that space is not even infinite either, but it looks to me that they are then applying an abstraction to an abstraction and find a false truth.

Back to infinity, because in the artificial realm it is fairly easy to work with infinity. We just set the computer program to accept the possibility of working with infinity and it has become a fact -- in that artificial reality. I've been told it can actually help us see things we would not have been able to see if not for infinity in the artificial reality.

I believe it was Isaac Newton who presented us with the artificial reality in which we can apply mathematics, including working with a negative 1. I am not aware of any negative 1 in nature, only in the artificial realm.

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Lastly, there are two mathematical systems that can do the same: the binary system and the decimal system. They can do all the other can do, yet numbers 0 and 1 are not identical at all.

Number 1 in the decimal system is used for 'unit' and 'unity', but number 1 in the binary system is better declared with 'on' in opposite to 'off'.

To have the term 'unity' expressed in the binary system, we need to agree on what set of numbers represent unity, for instance, 11100100. As long as we agree on this, then that set of numbers will represent unity.

And this shows that the decimal system is an agreement as well. We humans established a convention with ten digits and have been working with it ever since.

The fun part is that there are two sets of ten:

• The set that we count with using our fingers
• The set that starts with 0 and ends with 9

It means that when we say 'first' that this can then mean 1, but it can mean 0 as well. Perhaps that is why the terms first, second, third, etcetera, got invented to work around the 1 and 0 problem.

Good question, therefore. There is lots to see when mathematics is recognized for what it is -- an abstract method to declare very important things.

Speaking about physics Cosmology is still here astronomy quantum physics you name it Theoretical physics as well Dangerous thing is to bring up religious subject mentioning science Does the car making involves any act of God? Neither does the science Its a tool but has a variety of rules and if I begin listen to myself only I will miss the wonder of the science That's what I think about it Was nice talking to

There are plenty of mathematical constructs that are irrelevant to physics, e.g., homological algebra, class field theory and much of algebraic number theory, elliptic curves over finite fields, etc., and that is before we get the the abstractions of category theory. Mathematics is not physics and mathematics in reality has nothing to do with physics. One of the best discussions one that fine is the address by Ricard Feynman on the question

https://www.cantorsparadise.org/richard-feynman-on-the-differences-between-mathematics-and-physics-c0847e8a3d75/

"mathematics is the foundation of all exact knowledge of natural phenomena" David Hilbert 1900

Dear Truman Prevatt ;

Is it possible to imagine that in our world a set of mathematical devices or a unique mathematical device has become the conceptual support of physics and that another unique device could have supported it from the beginning? In any case, we are witnessing the realization of a set of mathematical devices and, as we believe, other worlds may have other mathematical devices supporting them along with different physics.

But as you stated, the mathematical and physical mindsets apparently evolve in two different directions and are not necessarily intrinsically related to each other!

And my point is that every word that passes through our minds must have a reality in the world for us or at least have the potential to be realized! Isn't that so?!

Numbers

are the language of Mathematics

A cautionary tail about reading too much in the connection of mathematics and any scientific endeavor is Srinivasa Ramanujan. His life was popularized in the movie, "The Man that Knew Infinity." With no training - he made significant contributions to multiple areas of mathematics all in a vacuum. In his work he solved some heretofore unsolved problems others had struggled with for years. He had an incredible intuition and for his time the ability to handle the concepts of infinity - although the logical foundations to handle infinity were just being developed by Russell and other who were formulation the logical foundations of mathematics.

When G. H. Hardy got wind of Ramanujan, he brought him to Cambridge. The one thing Ramanujan lacked in his background was not the understanding of difficult mathematical concepts but the logical tools to establish formal proofs.

Why some like to think there is some sort of mystical connection between mathematics and physics, mathematics can and has been developed in a vacuum, devoid of any reference to physics. Today many areas of mathematics, algebraic geometry, algebraic number theory, category theory, etc. remain so. Mathematics is not about reality. It is about logical game where mathematical concepts are explored within a logical foundational setting. Physics on the other hand is a science devoted to better understanding the universe around us.

Major discoveries in physics would be imppossible without mathematical data Yes Mathematics can develop independently so what? Can Physics do the same? Empirical data does not constitute any physical theory Perception and intuition are not an equivalent of understanding and vice versa

ok, If our world had developed differently in terms of physics and physical foundations, in a way that the fundamental constants of physics had different numbers, wouldn't it be possible that mathematical systems that we currently do not correspond to a physical reality would then be compatible with the physics of that world? Of course, in that case, we have to ask why mathematics that has appeared in our world and in the minds of intelligent beings should exist, when it is of no use in the current world?!

This question seems to be and I quote Paul Gordon famous comment, "Das ist keine Mathematik, das ist Theologie." (This is not mathematics, this is theology.)

Mathematics is independent of the value of any physical constant - and current physics are questions if these values have been constants at all. We can only "see" so far back in time.

Mathematics is independent of physics. It just happens to be a tool that can be used by physicists. The test of a theorem in mathematics is the logical validity of the arguments that are used in the proof. One of the most famous and important theorem in number theory was Fermat's Last Theorem. It was very simple to state but was only a conjecture by Fermat and open since 1637. Many of the greatest mathematicians had tired and failed to prove it.

Three hundred and fifty four years later in 1991, Andrew Wiles put the finishing coats on his proof and announced his results, only to have the referee of the journal he had submitted the paper to find a statement he made in the proof not to be logically developed. With the collaboration of one of his former graduate students, Richard Taylor, Wiles found a way around the mistake in the original paper in 1993. He rewrote his paper and published it to great fanfare.

That is how mathematics works. The basic foundations of mathematics starts with mathematical logic, set theory and the natural numbers. From the natural numbers, the integers are developed and from the integers the rational numbers are developed. From the rationals, quite a bit of work along with the development of topological concepts of closeness, convergence and continuity are developed along the way to the real numbers. The In order to handle sets with infinite numbers of elements, the natural numbers have to be extended to the cardinal numbers and the ordinal numbers and arithmetic on natural numbers extended. For example, cardinal numbers are used to assign the number of elements in a set. The set {a,b,c,d} has a cardinality of 4 - four elements. How many elements does in the set of natural numbers {1,2,3, ...}. It turns out that required the cardinal numbers to be larger than the natural numbers and contain the natural numbers as a proper subset. The answer, is the cardinal number aleph-null, from. George Cantor went on to fully develop the cardinal numbers, aleph-0, aleph-1, aleph-2,....

Because of the subtle structures of infinite sets, and the paradoxes that arose early on, e.g., Hilbert's Hotel, are very firm and rigorous based on logical foundations was required for the development of mathematics.

For the solution to the Hilbert's Hotel paradox,

https://www.youtube.com/watch?v=Uj3_KqkI9Zo

However, the cardinally of the Real numbers is infinitely larger than the rationals.

I wonder what Kurt Goedel had to say? According to this view, which became known as formalism, mathematics should be regarded as being, at heart, nothing other than a collection of formal games, each one played according to completely specified rules' My question is why natural sciences do not use Theology at their basis that'd be useful too wouldn't it?

I personally view mathematics as a kind of logical language — not reality itself, but a framework of symbols and syntax through which we speak about reality.

But just like we haven't seen the entire universe, we haven't “mathematized” all of it yet. For example, we still don’t fully understand how quasars behave at the very edge of the visible universe, or how momentum and energy are transferred in extreme regimes near them. So in that sense, we are still building the language with which we speak about the cosmos.

I believe mathematics is like a vocabulary, with internal grammar and structure. We use it to construct meaningful statements about the universe. Just like natural language allows us to form infinitely many sentences from a finite number of words, mathematics might allow us to explore an infinite universe — even if we only have access to a limited set of tools right now.

So yes — I believe mathematics is a linguistic interface to the physical infinite. Not yet complete, not absolute, but evolving with us.

This is a brilliantly articulated question that touches the very metaphysical boundaries of modern physics. I personally align with the view that not every mathematically consistent system necessarily maps onto physical reality. Nature, in my opinion, selects from the mathematical landscape not by logical permissibility alone, but by deeper constraints—energetic, geometric, and perhaps even information-theoretic.

We often treat mathematics as the “language of nature,” but it may be more accurate to see it as the toolbox we reach for when attempting to model observed behavior. The limited success of certain frameworks—like differential geometry in general relativity or Hilbert spaces in quantum mechanics—could reflect deeper physical symmetries and invariants, not just cognitive biases.

Moreover, mathematical pluralism opens an intriguing ontological door: are the “unused” frameworks just unphysical, or do they correspond to universes with entirely different fundamental conditions—disconnected from our observable cosmos?

In short, I’d argue that physics isn’t a passive decoding of a prewritten mathematical script, but an active negotiation between empirical regularities and formal abstraction. And that negotiation may be far more constrained than most mathematical pluralists assume.

— Adam Dakhil Nasser