What is the relationship between Mathematics and Physics?

[ramstin]

What is the difference between Mathematics and Physics?

 

[JasonRox]

Is this even worth answering?

There is a big difference between the two, so if you can't see that difference maybe you should be studying someth...

 

[ramstin]

"so if you can't see that difference maybe you should be studying someth..."

Mabey that is why I am here... .....................................
Yes, I am currently talking algebra classes at the local college. I have been looking for a bigger difference or better explanation other than the " one deals with the physical and one dose not need to" answer.

 

[Pengwuino]

Well there isn't much to say about the differences. Math is just math, it doesn't need physics to exist, its simply counting numbers ... along with a lot more complex things. Physics, on the other hand, is the modeling of the physical world around us. Physics uses mathematics to describe the world around us.

 

[simon009988]

math relies on a set of postulates and logic to prove something, where as physicist use experimental results to "prove" something

 

[Cosmo16]

math relies on a set of postulates and logic to prove something, where as physicist use experimental results to "prove" something

That isn't really correct either- a lot of phyics is proved theoreticly without experimental data. Proved using mathmathiimatics.

 

[Pengwuino]

That isn't really correct either- a lot of phyics is proved theoreticly without experimental data. Proved using mathmathiimatics.

Well something is never really proven in physics until an experiment confirms it and even at that, its never 100% proven.

 

[JasonRox]

Well something is never really proven in physics until an experiment confirms it and even at that, its never 100% proven.

Well, you have Applied and Theoritical Physics... don't forget that.

 

[cepheid]

That isn't really correct either- a lot of phyics is proved theoreticly without experimental data. Proved using mathmathiimatics.

Ummm...no. Physical theories are formulated mathematically to describe the physical world. That doesn't mean that anything has been "proved" about physics though. If they are good theories, then they should be predictive, i.e. one should be able to go out and do an experiment that may or may not bear out the predictions of the theory. If it does, then that lends credence to the theory. On the other hand, if it the experimental results are inconsistent with the theoretical predictions, the theory is scrapped, even though it was mathematically correct and self-consistent. I hope that this illustrates the difference between science and mathematics.

 

[dextercioby]

What is the difference between Mathematics and Physics?

I can't tell you that, but i can tell you the similarity between Theoretical Physics and Mathematics: they have isomorphic Lie algebras...:tongue2:

Daniel.

 

[ramstin]

"they have isomorphic Lie algebras..."

Way over my head. O.k. so Physics is the modeling of the physical world. Mathematics deals with theories and logic to prove something. Once you get into Theoretical Physics then you start to blur the line between the two. Is this correct?

 

[bao_ho]

Mathematics and Physics are two different classes you can enrol into.
The goals are the same. Make sure you pass the exams.
The contents will surely be abit of this and abit of that.

 

[matt grime]

Theoretical physics is still a model of the physical world, it is just one that is not necessarily testable by experiments (though it might become so later). Mathematics is the study of maths, phyics the study of physics, there really is no nice absolute clean line drawn between the two, and no nice set of rules for saying what either one is (we can usually say what it isn't). But as someone once said: i might not be able to define it but i know it when i see it.

 

[TheDestroyer]

Very nice question ! I'm answering as a physicist, the answer is that there is no different in fact, because the physics is called the in past the mathematics of the nature, and in this century we see that mathematics has become bigger and bigger and reached a very giant levels, that's why they spreaded them into 2 parts named physics and mathematics,

and if you can observe this, every physics scientist is a mathematics scientist also, like Gauss, Airy, Fresnel, ... and too many others, while you can't see or in little cases that chemistry people aren't friends with maths or physics, and the one who hate mathematics will hate also physics

AND TAKE THIS FOR NOTE, THE PHYSICIST WHO HATE OR DON'T LIKE MATHEMATICS IS A LOOOOOOSER, AND CAN DO NOTHING WITH HIS SCIENCE :P thanks for reading my nonsense :P:P:P:P

 

[matt grime]

I must protest, as a mathematician, that not all physicists are mathematicians. Using a subject does not make one a student or researcher of it. Frequently the need to distinguish between the two is unhelpful, and do not forget that we have the handy phrase mathematical physics. Is someone looking at open-closed conformal field theories doing maths or physics?

But someone who experiments with, say, semiconductors is not in general attempting to prove anything about mathematics, nor contribute to the study of mathematics as a subject.

 

[bao_ho]

what is "the study of mathematics"?

 

[simon009988]

I guess that mathematical ideas is just the study of relationships between numbers ,shapes, etc and does not nesessary go about to explain the physical world.

where as physics just use math as tools that seem to fit and predict outcomes of the physical world

 

[bao_ho]

where do these "numbers ,shapes, etc" come from?

 

[simon009988]

i guess they are abstrations of the physical world, like for example, i don't think it is possible to physically create a flawless circle but on an imaginary plane you can; and there is no such thing as an infinite plane in the world but math allows it to do geometry on and find proofs

 

[bao_ho]

by imagining this plane, have i not created it?

I do not believe that any bits of my brain is out of this world.

 

[matt grime]

The study of mathematics is, self referentially, what mathematicians do. I did say there was no nice simple answer.

 

[Cosmo16]

Ummm...no. Physical theories are formulated mathematically to describe the physical world. That doesn't mean that anything has been "proved" about physics though. If they are good theories, then they should be predictive, i.e. one should be able to go out and do an experiment that may or may not bear out the predictions of the theory. If it does, then that lends credence to the theory. On the other hand, if it the experimental results are inconsistent with the theoretical predictions, the theory is scrapped, even though it was mathematically correct and self-consistent. I hope that this illustrates the difference between science and mathematics.

Sorry,the use of "proved" that was more word choice then anything else. It was a horrible one though.

 

[robert Ihnot]

Newton is an interesting case. I had a professor once who refused to consider him a mathematician since he, "Was only interested in Physics."

He seemed to have invented quite a bit of math and held the chair of mathematics at Cambridge. It was Leibniz, who said, "Taking mathematics from the beginning of the world to the time when Newton lived, what he did was much the better half."

Yet it is true that he did not publish in pure math, and often ignored in math books.

This may have bearing on what is being discussed in this thread.

 

[D H]

Many physicists are directly involved with making weapons of war. Those who are not making weapons know that their developments may well be used to create new weapons in their lifetime. Physicists in general do not have a problem with this.

Mathematicians, on the other hand, are rarely involved with making weapons. They do know that what they create might well be used to make weaponry. This bothers the heck out of them even though this probably will not happen until long after they die.

 

[robert Ihnot]

DH" Mathematicians, on the other hand, are rarely involved with making weapons.

I don't know exactly how true this is. There have been plenty of people with math degrees who have worked on weapons. (Then there is the area of cryptology, which prefers mathematicians.) On the most creative level, no. Research in math is impractical and removed from the finished product in many cases. The military prefers engineers for most of it.

There is the case of Norbert Weiner. He is supposed to have developed the "heavy math" involved in the InterContinental Ballistic Missile, if I remember right. But no one makes a point of that today. Weiner says this:

One of the chief duties of the mathematician in acting as an adviser to scientists is to discourage them from expecting too much from mathematics. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Wiener_Norbert.html

 

[marsCubed]

hello all, this is my first post, i hope that the answer below helps someone understand this subject a little more.

Mathematics and Physics are not the same thing, although physics does employ mathematics to make it's models of nature.
For a mathematican the 4th dimension (for example) is an extension of cartesian space into the complex plane.
For a physicist the 4th dimension is bound up with space time as with Einstein's special and general relativity. The math the physicist employs is actually quite different as it is necessarily constrained by the behaviour of natural phenomena, a limit to the velocity of light, time dilation etc.
Mathematics, on the other hand, has no such constraints, it is limited instead to various infinities and singularities which arise out of the numbers alone.
There are ways to talk about one in terms of the other, but the difference is more than can be accounted for by simply substituting labels.

 

[monoceros]

I will let xkcd answer this: http://xkcd.com/435/"

 

[vociferous]

I would like to state that the major difference between mathematics and science (including physics) is philosophical.

The basic philosophy of mathematics is that something must be proven deductively using logic. It is constructive, id est, a mathematician must start with axioms and construct a proof. In mathematics, inductive logic is sometimes used, but generally discouraged. If you add a billion odd and even numbers together and they all equal an odd number, that is not sufficient to say that the sum of an even and odd number are always odd.

Likewise, many sciences like physics rely on deductive reasoning. Physics is probably the more mathematical science, and it relies heavily on proofs. But in physics, a proof is considered insufficient, because; it must conform to real observation. You could prove that a 20 foot perimeter fence, when made into a square shape, will enclose an area of 25 square feet, but a true scientist would not be satisfied that this is true until he actually tests the theory in the real world by experimentation and measurement. Science is deconstructive; it uses inductive logic. Scientists look at the world as it is, then try to figure out how it works by formulating theories. They then test their theories through experimentation.

Einstein proved his theory of relativity using mathematics, but it could not be accepted as true, from a scientific standpoint, until experiments were performed to test it.

So, to finally answer your question, physics makes use of mathematics to model real-world phenomena, but it is not mathematics, nor is mathematics physics.

 

[kenewbie]

Newton [..snip..] held the chair of mathematics at Cambridge.

This is quite common, as far as I can tell. Hawking now has Newtons chair, and he is not exactly known for his contributions to math.

When things get complicated, the lines get blurred. Does it really matter if a mathematician chooses his area of research by what *math* he finds interesting, or if he finds an area of another field which are lacking in mathematical tools and tries to develop some? The end results are the same, really.

k

 

[maze]

Many physicists are directly involved with making weapons of war. Those who are not making weapons know that their developments may well be used to create new weapons in their lifetime. Physicists in general do not have a problem with this.

Mathematicians, on the other hand, are rarely involved with making weapons. They do know that what they create might well be used to make weaponry. This bothers the heck out of them even though this probably will not happen until long after they die.

That's a nice sentiment, but it's just not true.

Archimedes, perhaps the greatest mathematician of all time, developed and improved the design of several siege weapons (catapult, etc).

Von Neumann's did substantial work on the mathematics of hydrodynamics during his work on the Manhattan project. He used this to calculate, among other things, the exact height to detonate the atomic bomb so as to cause maximum damage.

Turing helped break the Enigma code so as to help the US find and sink submarines.

Pontryagin's work on control theory and dynamical systems was immediately used for ballistic missile trajectories.

 

[matt grime]

For a mathematican the 4th dimension (for example) is an extension of cartesian space into the complex plane.

No it's not.

 

[HallsofIvy]

Very nice question ! I'm answering as a physicist, the answer is that there is no different in fact, because the physics is called the in past the mathematics of the nature, and in this century we see that mathematics has become bigger and bigger and reached a very giant levels, that's why they spreaded them into 2 parts named physics and mathematics,

and if you can observe this, every physics scientist is a mathematics scientist also, like Gauss, Airy, Fresnel, ... and too many others, while you can't see or in little cases that chemistry people aren't friends with maths or physics, and the one who hate mathematics will hate also physics

AND TAKE THIS FOR NOTE, THE PHYSICIST WHO HATE OR DON'T LIKE MATHEMATICS IS A LOOOOOOSER, AND CAN DO NOTHING WITH HIS SCIENCE :P thanks for reading my nonsense :P:P:P:P

I'm glad you recognize that this is nonsense. I was concerned until I read your last line.

Every physicist uses mathematics- that is very far from being a mathematician. And liking mathematics also does not make one a mathematician.

 

[dx]

To do physics you need to look at the world closely. To do mathematics, your common experience is enough.

 

[madmike159]

hello all, this is my first post, i hope that the answer below helps someone understand this subject a little more.

Mathematics and Physics are not the same thing, although physics does employ mathematics to make it's models of nature.
For a mathematican the 4th dimension (for example) is an extension of cartesian space into the complex plane.
For a physicist the 4th dimension is bound up with space time as with Einstein's special and general relativity. The math the physicist employs is actually quite different as it is necessarily constrained by the behaviour of natural phenomena, a limit to the velocity of light, time dilation etc.
Mathematics, on the other hand, has no such constraints, it is limited instead to various infinities and singularities which arise out of the numbers alone.
There are ways to talk about one in terms of the other, but the difference is more than can be accounted for by simply substituting labels.

I think this is the best explanation for it. Maths is used to help explain physics in a way you couldn't in words. We can understand classical physics without maths (most of the time) because it is just predictions about every day things. When you start talking about other dimensions, infinity and sub atomic particles we can't imagine it. Maths can be used to describe these things which we can't see/imagine.

 

[EsX_rAptOr]

The best way to tackle this dilemma is to think of Mathematics and Physics as follows:

Mathematics is the science of patterns. That is, it is completely based on logical and general abstractions of reasoning. All of its principles are solely founded on the relationships between these abstractions or patterns--it takes nothing else into consideration, but it rather pulls itself up from its shoelaces, so to speak. It is an ideal or romantic science, if I may.

Physics is the science of the reality we live in; it is a means to the understanding of the mechanics of this realm. It makes use of the great tool of Mathematics to corroborate itself in terms of the actual, empirical observations carried out and collected by Physicists. But unlike Mathematics, it is factual rather than purely logical; Physics does not necessarily have to be logical (think wormholes).

One is perfect, the other is real. But since we live in a universe that is far from perfect and like to compare real things to perfect models, Mathematics and Physics go hand in hand like twins.