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The New Mathematics

". . . as to the knowledge that they (i.e. relaxation methods) presume, the answer is that we have regarded no problem as solved until, for the actual computations, no more than the first four rules of arithmetic is required. What is of greater importance, even though a computer may not comprehend the theoretical basis of his calculations he will have, throughout, a mental picture of what he is doing; he will see his task as that of bringing unaccounted or 'residual' quantities within a specified margin of uncertainty. Whether regarded philosophically or practically, this is the essential feature by which the new mathematics differs from the old; it is 'mathematics with a fringe.'" PROFESSOR R. V. SOUTHWELL (Ref. 7)