Application of Mathematics

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This might be a very stupid question but comes to mind when we encounter each and every topic of pure maths. Why we are studying this, what are the applications of this etc etc. The topics in the pure maths are abstract unlike applied mathematics. What will be the best answer satisfy a student of mathematics, to the question application of mathematics? Actually our mathematics teachers generally dont focus on applications in mathematics. Does this mean that mathematicians are more interested in the extension/generalization of previously known field or results rather than their applications?

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In fact the importance of mathematics comes from its influence on our life. You may ask for example what is the importance of derivatives. I will answer you, don't you like maximizing your gains and minimizing your costs if you are a merchant for example. Don't you want to maximize the area of the land if you are an english or spanish immigrant to America with Coulombs at $16^{th}$ century. In that case you have to derive $xy$ and use constraints to express $y$ by means of $x$. You are doing mathematics. I did not speak about the number of times you used adding and substituting operations, almost every time you need to buy more than one thing. etc etc etc ...