It has been observed of late that most institutions tend to prefer Industrial (Applied) mathematics to pure mathematics; whereas, in the early years it used to be pure mathematics that was preferred. We have witnessed growth technologically, is this as a result of the preference for industrial (applied)mathematics?
Pure mathematics is like the banks of the river and Applied mathematics is the flowing water. It cannot cross the boundary but will always flow in between the banks. Both are interrelated.. But in my sight... Pure mathematics is the answer...
A Pure mathematician dreams even beyond the imagination of human beings... it is the technologists and scientists to apply them.... so Pure mathematics is the answer...
Very soon, I shall post an article on Mathematics, which will prove that my answer is 100% true...
The line between Pure and Applied Mathematics is very thin in modern mathematics, and will even become thinner as research advances. Besides, what is Pure today becomes Applied tomorrow. Therefore, both are needed for technological advancement.
Sorry to take a contradictory view, but I would think that pure & applied math have very, very little in common. Engineering mathematics is plagued with approximations, with simplistic models of reality (as in finite element analysis), it does not seek to find answers to questions related to any underlying reality - it only seeks to find some coarse model that somehow works.
Pure mathematics, as exemplified e.g. by recent Fields Medalists' work (Monastyrsky et al.) delves into the deeper nature of reality. David Hilbert said, a few decades ago: "We are often told that pure and applied mathematics are hostile to each other. This is not true. Pure and applied mathematics are not hostile to each other. Pure and applied mathematics have never been hostile to each other. Pure and applied mathematics cannot be hostile to each other because, in fact, there is absolutely nothing in common between them."
Pure mathematicians establish certain facts that applied mathematicians depends on. So, moving forward in terms of technology, both areas must continue to receive attention. Contribution to knowledge and research must continue as far as pure mathematics is concerned.
If I remember correctly, this comment regarded the residue theorem. Our complex variables professor, EE department, said, "EEs used this theorem for years and years, and then finally the mathematicians put in enough epsilons and deltas to prove it was correct."
Still, my vote goes to pure math, in answer to the question. Applied math is great and essential, but true breakthroughs require paradigm shifts. Of course, not to say that everything pure math investigates must become useful. It probably won't. But that's still how you find the gems.
In fact the advancement of theoretical or pure mathematics leads to the usage and applicability of it in applied fields. One example, the creation of Boolean algebra as a theory of thought and logical reasoning lead to the application of it in circuitry systems . Conversely, several new theories of mathematics were developed to address unsolvable problems in applied fields. Therefore they both equally enforce the advancement of each other as dear Stoica and others put it.
In my perception Applied mathematics has more reach to the scientific knowledge, as it clarifies the researched knowledge and converts into pragmatic approach whereas pure mathematics might be good for the exercise as well as academic purposes but in down to earth approach might be missing the popularity.
BOTH PURE AND APPLIED MATHEMATICS DRIVE TECHNOLOGY IN MY OWN OPINION
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