What does "theory" mean in the context of maths (like set theory, number theory, etc)

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Jignesh77

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What does theory mean in the context of maths, for example set theory, numbe theory etc.?
Does the word has the Same meaning as used in science?
Thanks.
 
Hello. Have you tried looking up definitions online? For example, you could google keywords define "theory" in mathematics. Please feel free to post any questions that may arise, after reading some definitions. To consider your second question, you could try the same search using 'science' in place of 'mathematics' – then compare and contrast the results from both.

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The "theory of relativity" is not a mathematics theory!

Jignesh77, as Steven G implied, in mathematics "Theory of" is equivalent to "Study of".
 
Shiloh said:
The "theory of relativity" is not a mathematics theory!

Jignesh77, as Steven G implied, in mathematics "Theory of" is equivalent to "Study of".
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In the Sciences a theory is a hypothesis that has been "tested many times." (It usually also makes predictions that the hypothesis structure did not predict.) In that, Relativity is indeed a Physical Theory. However it is an example of a transformation group in Differential Geometry (called the Poincare group for Special Relativity) so I actually think of it more as a model rather than strictly a theory.

-Dan
 
paul paner said:
yes i think it has the same meaning cause it has the same concept
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Theory in Mathematics isn't quite the same as theory in the Sciences. (My apologies to those who call Mathematics a Science.) In Mathematics, as stated above, theory is more of a set of studies. You study Number Theory. But in the Sciences a theory is an advanced sort of hypothesis; it is tested (and is testable) based on what Nature tells us. So, something like Number Theory is a field of study based on logic, but Special Relativity is a set of tested facts based upon experiment. The concepts are different.

-Dan
 
blamocur said:
My definition matches that of Wikipedia, i.e., a bunch of theorems deduced from a (usually small) set of axioms.
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Yes, but there are any number of concepts in Physics that make all sorts of sense, based on a set of axioms, that aren't actually realized in Nature. Isospin is my favorite. There really isn't a reason why it shouldn't exist. (Aside from the fact that we have too many quarks. But there isn't really any reason we couldn't have it. It's just that Physical Law restricts it.) And I hate to say it, but it's quite possible that String Theory, which is based on a beautiful set of "this makes a lot of sense" axioms, might have no bearing in reality at all. We'll have to wait until we can actually get some measurements.

-Dan
 
topsquark said:
Yes, but there are any number of concepts in Physics that make all sorts of sense, based on a set of axioms, that aren't actually realized in Nature. Isospin is my favorite. There really isn't a reason why it shouldn't exist. (Aside from the fact that we have too many quarks. But there isn't really any reason we couldn't have it. It's just that Physical Law restricts it.) And I hate to say it, but it's quite possible that String Theory, which is based on a beautiful set of "this makes a lot of sense" axioms, might have no bearing in reality at all. We'll have to wait until we can actually get some measurements.

-Dan
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Yeah, math theories are usually way ahead of practical implementations. Galois fields and Fourier series and transform were defined in the early 19th century but, AFAIK, had no practical applications until mid- or late 20th century.
 
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