Are math and physics fundamentally different?

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If yes, they are different in what ways?
Math is a collection of systems for making inference preserving metaphors. It often makes use of numbers, but not necessarily so. The mapping between a system of math and the system it is being used on isn’t universal. Something that may be mapped ton infinity for one system might not be mapped to infinity for another.

Physics models are often mathematically based. It’s possible to describe some physical phenomenon without using math, but you’ll find that such descriptions will be a bit crude. So in general you’ll find physics to involve heavy application of math just as accounting may involve application of math. But I would not say that physics in math.
 
If yes, they are different in what ways?
Maths is the purely theoretical study of numbers
1+1 = 2. that applies whether you are talking about atoms, people, gallons, photons, data in a computer or anything else.

Physics is the study of the basic laws of nature in the physical universe around us, from the gravitational interaction between galaxies, to the interaction of sub-atomic particles.

Physics makes extensive use of the language of mathametics to develop models and theories to explain the physical world and then test the assumptions in those theories and models.
Physics is one application of mathematics to the real world. others include accountancy, stastics and many others.
 
Math is the language that physics is written in.

Physics is the description of the sensible universe written in the language of math.

Capisce:):)?

ICXC NIKA
 
Maths is the purely theoretical study of numbers
1+1 = 2. that applies whether you are talking about atoms, people, gallons, photons, data in a computer or anything else.
That’s applicable when you are using the mapping between digits a set sizes(set theory). For other mappings, such as those used for boolean algebra it’s a little different. 1+1=1. Also if some one is using a different number base the result could be expressed differently (under base 2 the expression 1 + 1 =10 evaluates as true).
 
Apparently, you have never heard of the battle between the physics and math departments.
 
Not if you looked at my report card. And I don’t mean that in a good way.
 
Math is the language that physics is written in.

Physics is the description of the sensible universe written in the language of math.

Capisce:):)?

ICXC NIKA
:thumbsup:IThat is the best short and simple explanation I can think of, and I have degrees in both.
 
I’d say math is an investigation into the beauty and symmetry of logic and numbers and similar abstract entities. A true mathematician is often rather happy that he’s found something so esoteric that there can be no application in the real world.

Physics is the application of math to the real world to discover how the world works. Physicists like to take the most esoteric parts of math and figure out how they apply to the world.

The great mystery in all this is why Math should so well fit the Physical world.
 
I’d say math is an investigation into the beauty and symmetry of logic and numbers and similar abstract entities. A true mathematician is often rather happy that he’s found something so esoteric that there can be no application in the real world.

Physics is the application of math to the real world to discover how the world works. Physicists like to take the most esoteric parts of math and figure out how they apply to the world.

The great mystery in all this is why Math should so well fit the Physical world.
No mystery at all.

Mathematics was discovered by physical heads attempting to quantify the physical world.

ICXC NIKA
 
If you think long and hard enough about it, math is at the bottom of all knowledge. There is not a thing, action, or thought that can be expressed without using numerical symbols. Even the name of God is a word composed of the letters g-o-d, which appear in this numerical order of letters in the English alphabet: 7-15-4

As Paul Dirac put it:

“God is a mathematician of a very high order and He used advanced mathematics in constructing the universe.”
 
Math is the language that physics is written in.

Physics is the description of the sensible universe written in the language of math.

Capisce:):)?

ICXC NIKA
My wife is a physicist, and I am an engineer.

As we both describe it, physics is math with units, and engineering is physics with dollars involved 😉
 
I do not believe that they are so different on the fundamental level, after all, physics is math applied to physical phenomena. I like to think that Mathematics is math for the sake of math, while physics is math for sake of reality.
 
Why is math (a very non-physical discipline) such an excellent match in describing the physical world? Why is the physical world so mathematical?
 
Why is math (a very non-physical discipline) such an excellent match in describing the physical world? Why is the physical world so mathematical?
That’s turned around; it’s math that is physical. Math is the effort of the physical human head to understand and quantify the physical world.

ICXC NIKA
 
… it’s math that is physical. Math is the effort of the physical human head to understand and quantify the physical world.

ICXC NIKA
Still, you have not made an argument why math should be so good at describing the physical world. After all, I could argue analogously that psychology is the effort of people with psychological minds to describe how their minds work–and look at how little progress they’ve made in coming up with good theories useful for describing the mind. Or economics–that even is based, in principle, on math–and yet economists come up with new theories all the time, and none of them do very well at predicting what is to come. Why does math work so well, even the parts that mathematicians know will be too esoteric to apply?
 
Why is math (a very non-physical discipline) such an excellent match in describing the physical world? Why is the physical world so mathematical?
The physical world is not so mathematical. Physics is just the formulation of the simplest models to explain measurable reality. Math is the simplest methodology to describe such models.
 
Still, you have not made an argument why math should be so good at describing the physical world. After all, I could argue analogously that psychology is the effort of people with psychological minds to describe how their minds work–and look at how little progress they’ve made in coming up with good theories useful for describing the mind. Or economics–that even is based, in principle, on math–and yet economists come up with new theories all the time, and none of them do very well at predicting what is to come. Why does math work so well, even the parts that mathematicians know will be too esoteric to apply?
Because quantification is part of the nature of the physical world, and it seems that our human head is innately capable of processing quantification (according to some neurological studies). Our human bodies embody the principles of physics, and our minds understand through our bodies. A longer lever exerts more force; that is how limbs work. Faster movement requires more energy; so we breathe more while running than at rest. Etc. Math is the language of quantification, which is in the nature of physics.

Psychology and economics are not so innately hard wired to our minds. Indeed, one could argue that for the mind to understand itself would require infinite recursion. As to economics, it uses math to the extent that currency is quantified; but other factors, such as value, arise from psychological factors, which are closer to chaotic.

Consider the trick that older children play on younger siblings, getting them to exchange a dime for a nickel (US). YS sees size quantification easily, but confuses it with value, which is an unrelated artificial construct for which we are not innately prepared. And OC takes advantage. No doubt something comparable happens in real world economics.

ICXC NIKA
 
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