Excerpt from An Invitation to Mathematics

A few years ago, the faculty of Swarthmore College abolished the requirement of a year's course in mathematics for the ab. Degree. During the discussions which preceded this action, the mathematics department felt called upon to give what justification it could for maintaining the requirement. It had to be conceded that the course usually offered, consisting of some-algebra, some trigonometry and some analytical geometry, could hardly be con sidered adequate for those for whom this course constituted the last formal occupation with mathematics. On the strength of a general conviction, rather than on the basis of actual experience, the statement was made that it would be feasible so to arrange the work for such a course as to open the possibility of gaining some understanding of the significance of mathematics, of its relation to other subjects of study and to human experience. It was suggested to the author that he produce such a course; this was the stimulus which started the work of which this volume is the outcome.

A second incentive was furnished by the frequent inquiries from varied sources for some means of learning why mathematics plays so important a role not only in science and engineering, but also in philosophy, why mathematicians so often look upon their work as a form of art, what significance the subject has for the modern world. The most natural answer to such questions was to say that there is no shortcut to the attainment of such understanding, that one desiring to acquire it has to travel a long and laborious road, beginning with the elements of the subject and proceeding as far as his ability will permit; in other words, that such insight is reserved for the professional mathematician. But this reply did not seem to be the only possible one. The feeling persisted that for a person who is willing to make a serious effort, there should be a way of acquiring sufficient comprehension of the nature of mathematics to enable him to understand without having a large technical equip ment, the place this subject occupies in the world of thought and that such understanding should form a part of the equipment of an educated person. Thus it appeared worth while to make an attempt at paving the way towards this end.

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