For example, in Queuing Theory such a huge amount of literature is available that for a new researcher interested to start working in this field, it is difficult to find a research problem that is actually geared to applications. In fact, in Queuing Theory, researchers have put forward enough of theory that would perhaps find no application.
@Hemanta, my whole work in automation and control area is based on mahematics and mathematical modelling! Mathematical findings and inventions are not an aim itself, but engineering would not exist without mathematical inventions! Applied math is real math!
For my opinion mathematics doesn´t aim predominantly at a certain application, it exists by itself. Later on it´s a pleasure to find applications for the work you have done.
But to confess, I´m no mathematician, I´m as a physicist a mathematical "user".
Here is one quick answer found on the web:
http://www.brightknowledge.org/knowledge-bank/science-and-maths/spotlight-on-maths/applied-vs.-pure-mathematics
While some won't agree, I think it at least states one thing correctly: if you work in pure math, applications are generally not your interest. In applied math you may still work solely on the mathematical side of the story, but the set-up of the problem you study is inspired (directly or indirectly) by some application.
I find myself to often work on a mathematical problem motivated by a practically important problem, but one single paper may not bring the world much closer to a solution; it may rather be that the motivating problem is modeled mathematically, its properties analyzed and characterized in various ways, and perhaps algorithms for its solution may be devised and experimented with as well. Work of this nature are still relevant, but they do not alone bring the problem to a solution.
@Hemanta, my whole work in automation and control area is based on mahematics and mathematical modelling! Mathematical findings and inventions are not an aim itself, but engineering would not exist without mathematical inventions! Applied math is real math!
I can not understand this question. Perhaps pure mathematics are incompatible with those applied? If they are compatible, both must exist, but both actually exist.
At a giver historical period, indeed pure math is done for its own sake, whereas applied math is math usually connected with study of physical reality, and have a practical flavor. However there are applied math which are just pure math, but connected with a specific physical problem.
At large, there is a phenomenon: The pure mathematics of the previous generation tend to become the applied math of the next generation. The phenomenon is seen as we witnessing a shift from the mathematics of the physical world to the mathematics of Biology, of the living systems and in general of the human itself. The analytical-element-wise mathematics are not appropriate for the study of living systems. We need some kins of holistic-structural mathematics, that leave intact the living system. I suggests that such mathematics is “Category Theory”. This was the purest math we know. Lately there are a lot of applications to living systems, psychology etc. This is nicely described by a saying of the late psychologist of McGill J. Macnamara: “Category Theory is for psychology, what was Calculus for physics”. Another paper that describes the importance of mathematics to Biology is: Joel E Cohen, Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better. PLOS 2004. (http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0020439)
Summarizing we should say the the division of math into pure and applied it is only valid for small historical periods. At large, the roles are interchanged.
I understand the question as "Should mathematics (and its findings) be aimed at applications? I don't think so. Mathematics has developed in sympathy with social and technological evolution and is closely linked with new developments, inventions and radical changes in our perception of the universe in which we live (e.g. General Theory of Relativity), but it is not and has never been totally dependent on these for its own development. Mathematics more than often provides the tools for these developments but are not 'developed' specifically to address applications. It can however grow in a symbiotic way with developments in technology. Mathematics can therefore quite fruitfully and independently expand by its own until someone uses it as an applied tool, and then...it becomes 'applied'.
It is an operational theory can be used in action research not in academic research as it is often used while making business decision
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