TITLE: what is the definition of Mathematics ?
QUESTION [8 upvotes]: we all study mathematics , and all of us learn mathematical methods to solve problems , we learn how to prove , how to think mathematically 
but the question is, what is mathematics ? how can we define it as a branch of science ?

REPLY [2 votes]: According to Wikipedia, mathematics is the study of quantity, structure, space and change,
as abstract and circular as that sounds (what do we mean by these words anyway?) However, classifying "what is math" in more concrete terms may be impossible, since it is too far-reaching and depends on who you ask.
Mathematics is done by inferring new theorems from old knowledge using well-defined jungement rules. What these rules are, and why they are accepted, varies between mathematicians. The study of these issues is refered to as the philosophy of mathematics.
Insofar as mathematics is a branch of science, it is not, as it doesn't rely on observational evidence (though some may contest this, see philosophy of mathematics again).