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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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