ABSTRACT

The preceding chapter emphasizes the fact that even the most rudimentary number ideas are highly abstract and require for their mastery the development of a complex series of processes of associative thinking. This chapter deals with a second characteristic of mathematics. By concentrating on a single aspect of experience, namely, quantitative relations, mathematics has developed methods of reasoning that are of the most general type. The mathematical sciences exhibit intellectual generalization at one of its highest levels. The methods of mathematics have a range of application which is universal.