
Applied mathematics is the relating of mathematical concepts and results to the real world. Among researchers, it has always been the poor relation of pure mathematics, ever since the beginning of the latter as a systematic subject with the ancient Greeks. Pure mathematicians have tended to look down on their applied counterparts as being somehow sullied with the impurities of the world. (This is an attitude perhaps inherited from the Greeks, who viewed mathematics, and indeed all of science, as something that should take place as far away from the corruption of real life as possible.)
Needless to say, this contempt for applied mathematics does not permeate the whole of society. The average person might tend to look on all mathematics as equally abstract, uselessly divorced from the practical world. Governments have, however, usually favoured applied mathematics when it comes to giving research grants, mainly because it is easier to explain the goals of a research project of applied mathematics in terms of shortterm material effects on society. This position is remarkably shortsighted; it overlooks the fact that applied mathematicians usually make use of pure mathematics that is already in existence; the only major advance in pure mathematics which was forced by the needs of applied mathematics or theoretical physics was Newton\'s development of the calculus, to enable him to solve the equations of planetary motion.
The two views need to be balanced. Applied mathematics, the ability to relate the abstract concepts of pure mathematicians to the world, is a gift which few pure mathematicians have. On the other hand, many of the major advances in science have come from making new applications of branches of pure mathematics which had already been developed with no thought of their possible application (and often, indeed, doubts that they would ever have any practical relevance). The prime example of this in the 20th century is Einstein\'s application of nonEuclidean geometry to the problems developing in late19thcentury physics to come up with his theories of relativity. SMcL 
