Abstraction as Bread and Butter

Published on 19 May 2012 Mathematics

I find the first pages of a book to be the most instructive ones for many reasons. When I look at a good book that I read many years ago, I still find those first pages more interesting and inspiring.

Recently, I started reading a new book, “A Book of Abstract Algebra”. Similarly, I found a very interesting statement in the introductory chapter:

Algebra at the more advanced level is often described as modern or abstract algebra. In fact, both of these descriptions are partly misleading. […] To what extent is it abstract? Well, abstraction is all relative; one person’s abstraction is another person’s bread and butter.

– Charles C Pinter, A Book of Abstract Algebra: Second Edition, pp. 1-2.

It is, indeed. There is a lot to think about the abstraction of abstraction.