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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?

Prince Khan
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    Although the question is really vague, I understand where you're coming from, and there is a book publish by the Czech Academy of Science and the Institute of Mathematics, and distributed by Springer blatantly titled "Applications of Mathematics". It's a journal highlighting applications of mathematics in almost every body of maths, ranging from vector spaces, to differential equations, to more basic things like straight line graphs, etc. Generally speaking, the greatest portion of applied mathematics occurs in physics, but for a deeper insight, consult this book, or something similar. – joshuaheckroodt Nov 15 '17 at 18:35
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    Even if a mathematics teacher does not focus on applications, it does not follow that mathematicians are more interested in the extension/generalization of previously known fields or results. Most research mathematicians are intensely interested in exploring what is unknown, even if their focus is on unknown mathematics rather than unknown things-that-are-not-mathematics. – Lee Mosher Nov 15 '17 at 18:52
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    This is not a mathematical question, and it can only attract opinion-based answers. That would be two reasons to close it. Of course, nothing will be closed for the latter reason: too many seem to feel flattered when they are asked for their opinion. And it's easier to have an opinion than to have a clue. –  Nov 15 '17 at 18:52

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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 ...

AlphaXY
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