When the context is science, the word "theory" means a logical/mathematical framework which tries to explain the phenomena. Infact in science "Theories" carry some "Claims" or "Predictions" while every sub-discipline of science could be presented in many number of theories. But in "Mathematics" the word "Theory" seems to merely refer to a sub-discipline of a mathematical field of study. For example I could call "Number theory" the discipline of "Studying Diophantine equations" or "Group theory" the "Study of certain types of algebraic structures(namely Groups)" or "Differential equation theory" the "The methods of solving differential equations".

Does the word "Theory" in mathematics have some special meaning like bringing some claims or predictions or is it just a reference to the mathematical sub-discipline we are studying?

  • $\begingroup$ I believe the second one is more appropriate. $\endgroup$ – Alessandro Blasetti Nov 9 '16 at 20:47
  • $\begingroup$ The analogue of the scientific term for theory in mathematics would be the term theorem, although they are very much distinct concepts and should only be thought of as analogous, not equivalent. $\endgroup$ – Dan Rust Nov 9 '16 at 20:54

Generally it's just a reference to the sub-discipline. There is also a technical meaning in mathematical logic.

  • 2
    $\begingroup$ Also don't forget that a "homology theory" is a specific algebraic construction satisfying certain requirements. But that's a special case. $\endgroup$ – Arthur Nov 9 '16 at 20:56

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