The Role of Abstraction


Posted on December 24, 2021

A quote from “Elements of Abstract Algebra,” written by Allan Clark

“Abstraction is simply the process of separating form from content. We abstract whenever we pass from a particular instance to the general case. Even the simplest mathematics, ordinary arithmetic, is an abstraction from physical reality. In modern mathematics we abstract from previous mathematical experience and reach a new and higher plane of abstraction. Indeed, each mathematical generation abstracts from the work of the preceding one, continually distilling and concentrating the essence of old thought into new and more perfect forms. The rewards are great. Not only does abstraction greatly enhance our understanding, it also dramatically increases the applications of mathematics to practical life.” xvii