Laws vs. Theorems

[jordanfc]

What is the difference between mathematical laws, such as the law of sines/cosines/tangents, exponents. logarithms, etc. and mathematical theorems (the binomial theorem, fundamental theorem of calculus, and pythagorean theorem). Do theorems ever eventually become laws or how is it decided if something is a law or theorem?

[Tom Mattson]

I always thought that "law" and "theorem" are synonymous in mathematics, but according to Math World's Entry for "Law" there is a slight distinction. But "law of cosines", et al, still qualify as a "theorem".

[doomtiki]

A law is something that is axiomatic and assumed to be true. A theorem is something that is deductively derived from a law or group of laws. For example, the Pythagorean theorem is critically dependant on Euclid's Fifth Axiom (the parallel postulate), which is an example of a law. A law is not necessarily always unchallengable. When Euclid's Fifth Axiom is negated, hyperbolic and eliptic geometries can exist.

[Tom Mattson]

A law is something that is axiomatic and assumed to be true.

 

This remark could be confusing, because neither the law of sines nor the law of cosines is assumed to be true. They are indeed theorems, and yet they are called "laws".

 

The MathWorld definition seems to be consistent with that.

[lurflurf]

It is best to not get too caught up in what different results are called. The various terms have connotations, but there are exceptions and inconsistencies. Don't get too caught up in whether something is a law, proposition, lemma, collorary, theorem, definition, or fact. Like they say "One womans theorem is anothers definition."

[BigMoosie]

In science arent laws and theorems the same? Just that laws was the old term that has stuck for things discovered hundreds of years ago?

[Graeystone]

Generally speaking, A Law is something that has been proven beyond a shadow of a doubt. (Thermodynamics, gravity). A Theory is something that still has questions that needs to be answered.

 

The problem is that sometimes in science, like many other things, there people who don't like the results, mainly they or others disprove their theory, so to get the desires they want, they do their hardest to 'get the rules changed'.

[JaKiri]

For example, the Pythagorean theorem is critically dependant on Euclid's Fifth Axiom (the parallel postulate), which is an example of a law. A law is not necessarily always unchallengable. When Euclid's Fifth Axiom is negated, hyperbolic and eliptic geometries can exist.

 

That's true of theorems as well, you know.

[JaKiri]

Generally speaking, A Law is something that has been proven beyond a shadow of a doubt. (Thermodynamics, gravity). A Theory is something that still has questions that needs to be answered.

 

That's not true. A scientific law is a postulate that can be expressed in a single statement, and has been empirically proven to be true. A theory is just as true as a law (in some comparisons, probably more so), it's just it's made up of more statements.

 

The problem is that sometimes in science, like many other things, there people who don't like the results, mainly they or others disprove their theory, so to get the desires they want, they do their hardest to 'get the rules changed'.

 

Eh?

 

In science arent laws and theorems the same? Just that laws was the old term that has stuck for things discovered hundreds of years ago?

 

There are no theorems in science. There are scientific laws and there are Theories (commented upon above), but both of those (in a scientific context) is something that has been observed to be true. If there is definite significant evidence that contradicts the known theories, then the theories are discarded or changed.

 

A theorem or mathematical law are things which are true given the axioms of the system - and cannot be disproven under those conditions.

[swansont]

Generally speaking' date=' A Law is something that has been proven beyond a shadow of a doubt. (Thermodynamics, gravity). A Theory is something that still has questions that needs to be answered.

[/quote']

 

 

I know JaKiri already addressed this, but it is so incredibly freakin' wrong that it needs to be pointed out again. Theories do not "grow up" to be laws.

[yialanliu]

Generally speaking' date=' A Law is something that has been proven beyond a shadow of a doubt. (Thermodynamics, gravity). A Theory is something that still has questions that needs to be answered.

 

The problem is that sometimes in science, like many other things, there people who don't like the results, mainly they or others disprove their theory, so to get the desires they want, they do their hardest to 'get the rules changed'.[/quote']

I disagree...nothing is proved beyond a shadow doubt! And I mean nothing well nothing in science!

[Graeystone]

Now go into a room filled with forensic scientists and say that.

[MetaFrizzics]

Now go into a room filled with forensic scientists and say that.

forensic scientist: "for-en-sick' - a scientist willing to accept money from a lawyer.

[cubexican]

I learned that a theorm is something that must be proven to be believed true and a law is something that must believed true without any proof.

[DQW]

I learned that a theorm is something that must be proven to be believed true and a law is something that must believed true without any proof.

This has been proven incorrect by counter-example : the Law of Cosines, for instance, should do.

 

Things that are believed true (and can not be proved) are usually called 'axioms' in math and 'postulates' in physics.

[cosine]

Mathematically speaking, laws are axioms and postulates, etc. In other words the assumed. Theorems are the results derived from laws. A "Theory" is a term to describe the large body of laws and theorems of a certain system. For example Euclid's Elements is a book containing a large part of Euclidean Geometric Theory.

 

Names of famous theorems can be confusing and may not actually satisfy what is implied by their names. The law of cosines is not really a law, it is a theorem. (Unless for some reason you based your system of geometry by making it an axiom, but that would be lame.) Pythagreas's theorem, while believed to be first proved rigorously by Pythagreas, was known well before his time.