Such matters as the growth of life insurance, the construction of the large navies of the eighteenth century, the economic and technological problems brought about by the opening of the industrial revolution on continental Europe, the present world-wide war atmosphere, and today’s concentrated effort to conquer outer space, have led to many practical developments in the field of mathematics. A division of mathematics into “pure” and “applied” has come about, research in the former being carried on to a great extent by those specialis’s who have become interested in the subject for its own sake, and in the latter by those who remain attached to immediately practical uses.