| Summary: | In the Introduction I explore the reasons for my enquiry, and outline the inadequacies of some of the existing attempts to determine the aims and purposes of mathematics in education. In Part 1 I discuss the scope and validity of the justification of mathematics on the basis of its supposed usefulness. From there I defend the view that, in principle at least, there are different kinds of reasons for learning mathematics. In Parts 2 and 3 I attempt to explain whether or not mathematics is fit for two particular non-utility purposes claimed by various writers, and if so, how. Thus, in Part 2, I examine the rather strong claim that mathematics is afine art, and hence or otherwise that it is a source of aesthetic satisfaction. In Part 3, I explore the claim that mathematics provides mental training. Here I shall show that 'mental training', is a broad notion ranging from the rather moral character training to the more restricted notion of training in logic. Between these extremes lies a more modest notion which I argue is the most plausible. The thesis is thus both a history of ideas and a clarification of the concepts used in describing fairly established purposes and rejecting those that seem to me to be unattainable or at least scarcely attainable by studying mathematics. The reason for the study is twofold. I see it as a particular case of the general enquiry into the aims of education. So that my conclusions should inform those who want to justify the place of mathematics on the curriculum. Also, however, I want to suggest that the purposes of mathematics education are internally related to understanding the subject, so that the pupil will gain understanding from a clearer notion of what he or she is doing mathematics for.
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