Mathematics is (quoting definitions 1.a. & b. from the Oxford English Dictionary, though important philosophical/academic definitions are elaborative/different*) 'the abstract science which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra;' and in a 'wider sense, includes those branches of physical or other research which consist in the application of this abstract science to concrete data. When the word is used in its wider sense, the abstract science is distinguished as pure mathematics, and its concrete applications (e.g. in astronomy, various branches of physics, the theory of probabilities) as applied or mixed mathematics'. Maths can be called the study of number, space & shape, and processes, as well as many other things such as pattern, order & chaos, and according to some mathematicians, entities, and everything.
Math can be applied to any subject, any problem or question. If maths cannot easily model a problem & answer, it will, and with formal language theory it can model any question, so maths brings objectivity into the subjective world. There are only two separate ways of looking at the world: mathematical, superstitional. Even science fully depends on maths, but maths does not depend on anything.
Maths is the vastest, most difficult, but most applicable and rewarding subject, and everyone should be a mathematician to some degree.
Mathematics is the subject that has been built up over millennia until it has actually become the vastest area of knowledge. Archaeology shows that foundational maths began for humans when primitive people counted on objects on which they carved tally marks. Primitive civilizations did arithmetic on objects on which they carved operations. Higher maths (philosophical/theoretical) began in ancient Greece when the rationalist idealist philosopher, scientist, mathematician Pythagoras started it and said 'all is number,' 'number rules the universe,' which Plato paraphrased, and we now similarly say 'everything is mathematics; mathematics defines reality.' Higher/theoretical maths, with more and more applications, has developed ever since, especially in the secularist Age of Enlightenment through the Age of Reason and Modern Age, in which maths expanded to the subject of (theoretical) computer science and the Computer & Information Ages, which brought new ways of doing maths.
It is important mathematicians have a decent understanding of the history of maths, which is an area of specialization for some mathematicians and historians.
*Mathematicists recognize dual aspects of maths can be defined (such as abstract & theoretical versus concrete & practical or 'existent') but prefer to call maths unified--including, in one system, both the basic defining/logical & conjectural/theoretical/law/proof statements of 'abstract' (pure/academic) maths and 'ontological' maths' 'concrete' existence as reality's objects & processes (so, despite the usability of such terms, this remains a monism, rather than a duality such as philosophy's 'abstract & concrete,' and is most focused on maths as a whole. One may wonder what the cosmology is that must go along with that ontology... of course, positing maths as the substance & essence of reality goes with a purely mathematical cosmos idea).