The standard model of particle physics is based on the maths of symmetry and symmetry breaking. Relativity likewise is derived from imposing a demand for general co-variance on nature - a global spacetime symmetry.

So it is a particular branch of maths that does the heavy lifting. And all physics reflects its essential natural logic.

You could consider symmetry and symmetry breaking as ur-physics rather than just a branch of maths. It is the "realty" that breathes fire into any equation, even QM. (And note an equation is a statement that encodes a symmetry, or unity, in terms of the components it can be broken into.)

My view is that QM is basically the Schrodinger equation (and it's offshoots), which is a symbolic mathematical equation used to predict the location of an election. What exactly is the equation describing falls within the realm of metaphysics,. Some scientists have speculated what this metaphysics might be (referred to interpretations), but such metaphysics is purely philosophical in nature. For myself, I consider the mathematical equations convenient tools to assist scientists in their processes of measuring and predicting within their tolerance levels. QM itself is entirely probabilistic which may provide some hints as to the stuff it is attempting to measure.

A question I would like to clear up is this. Does the Universe and the physical laws of physics happen because of math of QM or does the mathematics of QM just describe the behavior? — Mike

If it’s of help, another way of asking this: Is nature the language of maths or are maths a language of nature.

Science can’t answer this one. Neither can mathematics. But I like your question. Either answer, though, can result in quantity holding limitations upon what can be.

Myself, I’m of the opinion that maths are one of the many languages of nature. Nature’s Logos as some used to call it. Stated otherwise, I don’t uphold that maths are foundational to reality. For a more down to earth example, maths can quantify and measure music so that computers can produce music, but the vibe/soul/meaning/etc. of music (often resultant of indistinguishable variations that together harmonize into an expressive whole) can never be mathematically identified, even in principle. This, however, isn’t to say that others won't boisterously laugh at what I've just said via their opposite convictions. I agree with Rich, though: the issue is one of metaphysics.

Thank you for the responses. So far it looks like from what is being said most people believe that Physical Reality is the central cause of what we see. As @apokrisis says reality breathes fire into the equations. I also harmonize with the concept that math is just a descriptive language of nature. I guess I should have made this a poll. These responses have been helpful and I guess that the question has not been really answered by science as @javra has said "that science can't answer this". This is what I have really been wondering. Has the question been settled or not. So I guess it has not. So far most people seem to be of the opinion that math is just the language that helps us describe reality. That does seem sensible to me.

I guess now one has to wonder who or what has made the rules and the physical laws. I think that is probably another discussion entirely.

I guess now one has to wonder who or what has made the rules and the physical laws. I think that is probably another discussion entirely. — Mike

Such a discussion must first entertain that such Laws do exist or do the "rules of nature" evolve as does everything else. I would say there is no way to falsify such a doctrine and thus becomes its own metaphysical viewpoint.

Is nature the language of maths or are maths a language of nature.

Science can’t answer this one. Neither can mathematics. But I like your question. Either answer, though, can result in quantity holding limitations upon what can be.

Myself, I’m of the opinion that maths are one of the many languages of nature. Nature’s Logos as some used to call it. — javra

I thought nature/reality used mathematics like computers use code. It would seem silly to think the mathematics is fundamental and reality is then built on top of it because where would it exist "fundamentally"?

This sounds similar to the concept of universals and how they have some existence outside of the concepts that "the form" is inhabiting in reality. IE "the perfect triangle exist abstractly even though there are no perfect triangles in reality" I call bs on that.

I thought nature/reality used mathematics like computers use code. It would seem silly to think the mathematics is fundamental and reality is then built on top of it because where would it exist "fundamentally"? — intrapersona

Hey, I agree. But to some reality pretty much is equivalent to mathematics, thereby making nature the product of maths. For such, maths—or at least the quantity they address—becomes of itself a monistic substance of sorts, encapsulating both quantity and quality without exception. And it’s an old appraisal of reality: Pythagoras was the first recorded person affirming it, me thinks, and stands in contrast in many ways to Heraclitus (this being the guy who spewed mystical stuff about Logos).

This sounds similar to the concept of universals and how they have some existence outside of the concepts that "the form" is inhabiting in reality. IE "the perfect triangle exist abstractly even though there are no perfect triangles in reality" I call bs on that. — intrapersona

Animals exist in reality—and they’re distinct from plants in reality as well. Yet their both abstractions and universals; I say this while denouncing there being any such thing as a perfect form of either. Animals include particulars such as real cats and dogs. But cats and dogs are abstract universals as well. It’s only when one addresses a particular physical instantiation of an animal that you’re then addressing something concrete that isn’t a universal. But now, you’ve lost sight of what an animal is: a bird, a fish, an ant, a whale, a nematode, and even a sponge—all these are animals but none in its concrete presence establishes the reality of what an animal is. Yes, the universal of animal can hold relatively fuzzy borders to us epistemologically, but these borders become distinct when distinguished from the universal of plants. And again, both animals and plants are ontic--this, in part, via all their particular physical instantiations, none of which can on its own equate to the universal of “animal” or "plant".

Our abstraction of "animal" is the concept; the reality of animal-ity is the universal that exists independently of our concepts.

I’m anticipating disagreements. But I’m still upholding that universals are not bs. The headaches, btw, start only once you acknowledge their presence 8-) … this concerning issues of what governs what. It’s like an age old problem in anthropology: does culture govern people, vice versa, or both. It’s when you accept that it’s both that you venture into the perils of uncharted territory.

As to geometric forms, they’re not my foremost interest. Like up and down and the geometric expression of this dimension, I acknowledge that they make sense as universals as well. But I’d rather learn of your take on animals and plants being, or not being, real universals of which we hold epistemological understandings of. (Using what I said above; without use of Platonic forms as typically interpreted.)

At any rate, though they may seem similar—the idea of maths as monistic substance and the idea of universals—universals can well occur without need to be derived from a foundation of maths. … I so argue.

As far as I know the role of mathematics in science is by default considered to be that of modeling a certain part of reality: the idea is that we have mathematical models that work under some assumptions with some degree of correctness and we can always be forced to upgrade our model once we find some inconsistency (which already happened several times).
There are also more "foundamental" mathematical models that explains "descriptive" models, a classical example is the heat equation (descriptive model): you had the theory of heat as a "fluid" (foundamental model) and the theory of heat as energy in a system of particles (another foundamental moel), both models lead to the "heat equation" (descriptive model) but they "explain" it in different ways. And you can always go deeper and deeper considering your foundamental model just as "descriptive" and explaining it with a more foundamental one.

As far as I know the role of mathematics in science is by default considered to be that of modeling a certain part of reality: — Babbeus

Yes that's a good point. And we should not confuse the model with that which is being modeled, that would be like confusing the map with the terrain. But I think the issue here is that the math is not actually the model itself, it is the tool which is used to create the model and to interpret the model. Therefore we have a medium between the map and the terrain, and this is the mathematics. The mathematics is used to create the map and to interpret the map. But now the mathematics may be perceived as the medium between the creation of the map and the interpretation of the map, and some may mistakenly apprehend this as the terrain itself.

There's an easy (yet correct) answer to this: no. Mathematics isn't the cause of anything. Mathematics is simply an invented language for thinking about relations abstractly.

Mathematics is a tool to view a very narrow slice of what surrounds us. Scientists invent this tool to measure and predict to a level of necessary practicality for a very specific purpose. This narrow view of life cannot be elevated to a complete metaphysics of nature, especially when the equations themselves are necessarily in conflict because of their own peculiar nature.

There's an easy (yet correct) answer to this: no. Mathematics isn't the cause of anything. Mathematics is simply an invented language for thinking about relations abstractly. — Terrapin Station

So mathematics is a by-product of laws of physics which permit the representation of one physical system by another - i.e. laws that permit abstraction. Mathematics, apart from being extremely terse and efficient, also expresses physical laws in a manner most amenable to testing i.e. we have a powerful apparatus with which to make deductions from conjectured theories.

And, because there is no special physics unique to the human brain, we are able to automate much of the mathematical reasoning by instantiating the abstractions that interest us on a computer.

So mathematics is a by-product of laws of physics which permit the representation of one physical system by another ... — tom

More precisely, mathematics is an symbolic and convenient tool, a certain subset of which scientists convert into a Law, imbuing the equations with a certain quality of permanence and incontrovertibly such that no one dare to deny - until new equations are introduced. I wonder when the concept of a Law of Physics or Nature was first introduced?

I don't understand why you've started your comment with "So . . ."

You're not reading me to be saying what you wrote after "So," are you?

Mathematics is simply an invented language for thinking about relations abstractly. — Terrapin Station

But the relations are certainly not invented. Certainly the way we add things, and the number system we use, and so forth - they're invented. But the relation described by 1+1 = 2 can't be invented. What do you take to be the connection between relations and causes? What's the difference?

But the relation described by 1+1 = 2 can't be invented. — Agustino

Why do you say that this relation can't be invented? I see no other possibility except that it was invented. It's called counting, start with one, add another one, and you get two. "One" is invented to stand for something, and "two" is invented to stand for what you get when you add another "one' to the original "one". That is the entirety of the relation and it appears to be completely invented. What do you think I am missing?

Why do you say that this relation can't be invented? — Metaphysician Undercover

1+1=2 isn't a relation, it's a description of a relation.

It's called counting, start with one, add another one, and you get two. — Metaphysician Undercover

Counting is an empirical matter. It's only in our world that we count 1, 2, etc. We learn to count by putting objects together, and saying, one, two, etc. I can imagine worlds - for example a world where objects annihilate when they come into contact - because say the world is made out of both matter and antimatter. Beings in such a world would imagine 0 when they imagine two. For them 1+1 = 0 will be an accurate description of their world. Or perhaps they'd say 1+1=0 and 1+1=2 are both true. (depending whether one object is matter and the other is antimatter or matter)

1+1=2 isn't a relation, it's a description of a relation. — Agustino

What is described is the relation between these symbols, nothing more. It is order, pure and simple, 1, 2, 3, 4, etc.. That is why mathematics is so useful, these symbols do not describe anything in particular, they have a position within a created order, and as long as the order is maintained there will be no mistake. So the symbols don't describe anything at all, that's why we have a zero, but they can be applied to anything, and that's why they're so useful.

We learn to count by putting objects together, and saying, one, two, etc. — Agustino

I did not learn to count this way, and I bet that you didn't either. I learned that two comes after one and three comes after two, and so on. I very quickly learned how to count to ten, and then to one hundred. There was no putting objects together when I learned to count.

I did not learn to count this way, and I bet that you didn't either. I learned that two comes after one and three comes after two, and so on. I very quickly learned how to count to ten, and then to one hundred. There was no putting objects together when I learned to count. — Metaphysician Undercover

So how did you get to know what 2 means?

What is described is the relation between these symbols, nothing more. It is order, pure and simple, 1, 2, 3, 4, etc.. That is why mathematics is so useful, these symbols do not describe anything in particular, they have a position within a created order, and as long as the order is maintained there will be no mistake. So the symbols don't describe anything at all, that's why we have a zero, but they can be applied to anything, and that's why they're so useful. — Metaphysician Undercover

Yeah, and we could make alternative orders, only that they're not so useful at describing our reality.

For those interested, this is a relatively short and thorough introduction to quantum mechanics:

http://www.people.fas.harvard.edu/~djmorin/waves/quantum.pdf

So how did you get to know what 2 means? — Agustino

I told you, 2 means one more than one. Do you think that two has some other mysterious meaning different from this?

Yeah, and we could make alternative orders, only that they're not so useful at describing our reality. — Agustino

If it's not useful, then why would it get used. And if it wasn't being used it wouldn't exist. But there are different systems of order, natural numbers, fractions, decimals. rational numbers, irrational numbers, real numbers, integers, imaginary numbers, etc..

I told you, 2 means one more than one. Do you think that two has some other mysterious meaning different from this? — Metaphysician Undercover

How do you know what "one more than one" means?

The same way that I know the meaning of any common words by being taught by teachers, and observing usage. I was taught that one more than one is two, and that's how I know what it means.

The same way that I know the meaning of any common words by being taught by teachers, and observing usage. I was taught that one more than one is two, and that's how I know what it means. — Metaphysician Undercover

No you weren't. You observed usage and reality and saw that one more than one is two. But you could have seen something different.

You've lost me. I don't know what you mean by "observed reality". The reality I observed was that "one" and "two" were used in that particular way. How could I have seen something different when there was no such thing to have been seen?

For a more down to earth example, maths can quantify and measure music so that computers can produce music, but the vibe/soul/meaning/etc. of music (often resultant of indistinguishable variations that together harmonize into an expressive whole) can never be mathematically identified, even in principle. — javra

Can you elaborate on this? From what I know, music and its effect on us can be completely scientifically explained. You can play same tune in different scales and it will "sound" heavy, pop, oriental, happy, sad,...

For example, if you play a note at certain frequency together with another note at that frequency times X, the resulting sound will be "pleasant" only if X is sufficiently close (<1%) to a rational number with denominator lower than, let's say 15 (depends on how good our hearing is). This makes it easy to predict when two notes will sound harmonious, only by using mathematical language. Not only that, but we also have a pretty good idea, why it is like that.

Does the Universe and the physical laws of physics happen because of math of QM or does the mathematics of QM just describe the behavior? — Mike

The latter.

What is the cause of things like particle interactions and things like gravity and magnetism?

I don't know how far into the "cause" you are talking about, but I'll tell you from the point of Quantum Field Theory.

From the quantum chromodynamics' point of view, protons and neutrons are held together by "residual strong force". Proton and neutron exchange pions that keeps these two together. If you look even closer into it, gluons keep quarks together but also helps produce pions. You can consider this as particle interactions. So gluons are one of the many "force carriers".

Force carrier of magnetism is photons.

Theoretically, force carrier of gravity is gravitons. However, the existence of graviton has not been confirmed. It is a hypothetical particle.

I am trying to understand what the interpretation for this question is. I hear some people say that math determines the behavior of the physical universe while others say that math just describes the behavior. Has this question been settled?

Depends on the interpretation, but it is generally believed that math just describes the behavior. In light of new, better, and more compatible theory, the interpretation is subject to change. This is a philosophical aspect of physics, not science. I wouldn't go too much into it. I always keep an agnostic view of it. It's not that important either for science.