EVOLUTION OF MATHEMATICAL CONCEPTS 



and geometric form, took their first beginnings in 

 the practical interests of man living in the physical 

 world. Those mathematical concepts, and the 

 methods of dealing with them systematically, 

 underwent a gradual evolution in close connection 

 with the practical efforts required to grasp, classify 

 and characterize, and so far as possible to dominate, 

 the spatial relations of actual bodies, both in their 

 fixity and as changing in temporal succession. 

 The more closely men scrutinized the external 

 world, at first for practical reasons, and later from 

 intellectual curiosity as well, the more things and 

 processes they found to have aspects which are 

 measurable, and the more frequently they were 

 able to employ their nascent "mathematical processes 

 and concepts for the precise characterization of 

 physical objects and phenomena. However abstract, 

 and remote from their origins in sensuous experience, 

 great branches of Mathematics have become in 

 modern times, they all have their roots in the 

 primitive intuitions of time, space, and matter. 

 Mathematics was then in its beginnings essentially 

 a Physical Science, distinguished from other special 

 branches of Science mainly by the fact that the 

 universality and relative simplicity of those aspects 

 of the world with which Mathematics was primarily 

 concerned facilitated a comparatively rapid process 

 of schematization by abstraction. An effect of 

 such schematization was the gradual evolution 

 of an elaborate symbolism which, in modern times, 



