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Short answer:
To model the physical world as precisely as possible. If mathematics didn't have a useful purpose, it wouldn't be of much worth to us. Hence why focusing on real world applications helps in understanding its purpose.
Long answer:
The purpose of Math is to discover the properties of different relationships and to explain universal truths from a very basic set of commonly accepted belief system of numbers and symbols called axioms.
Mathematicians in general deduce explanations - as meticulously and accurately as possible - by knowing everything they can, pertaining to a particular circumstance; and the results are the derivatives of all the co-relationships from a set of axioms that form the mathematical explanation, also known as an equation.
The proof of results and the explanation given from mathematics, form the foundation of every scientific field. The vast majority of mathematicians don't care what practical applications their works have in relative to other faculties of sciences - although practical applications usually do evolve if the mathematical explanation is true - however mathematicians are infatuated with one objective; truth that the explanation produces.
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What is pure math?
Pure Mathematics is the branch of mathematics that deals only with mathematics and how it works - it is the HOW of mathematics. It is abstracted from the real world and provides the "tool box" of mathematics; it includes things like calculus. Applied mathematics is the branch of mathematics which applies the techniques of Pure Mathematics to the real world - it is the WHERE of mathematics; it includes things like mechanics. Pure Mathematics teaches you HOW to integrate, Applied mathematics teaches you WHERE to use integration.
What does mathematics have to do with math?
'Math(s)' is the shortened word for 'Mathematics'. The word 'mathematics' comes from Classical Greece, and means 'to learn'.
What are disadvantages of mathematics?
Only a person who does not understand mathematics is disadvantaged. Mathematics in itself has no disadvantages.
Does mathematics lie in physical sciences?
Mathematics is used extensively in the physical sciences, by mathematics itself is not a physical science.
Is mathematics science?
Depending on what type of science, yes mathematics can be science. Like if you're doing physics that can be mathematics.
