It’s reunion season and even though we were unable to have an official reunion, some of us got together last evening. Math was and is a popular major at St. Olaf, and it was fun to reconnect with some old classmates. I happen to have my Abstract Algebra book and nostalgia probably tugged it off the shelf for me today.
Come to find out the author wrote super interesting prologues to each chapter. Of course I couldn’t have been bothered with such unnecessary consumption of my time back when I was twenty. Getting the problem sets done was my minimal obligation! Now stories of Euclid and Niels Abel and Evariste Galois are the bits I want to hear about.
Education is wasted on the young!
Algebra today is organized axiomatically, and as such it is abstract. Mathematicians study algebraic structures from a general point of view, compare different structures, and find relationships between them. This abstraction and generalization might appear to be hopelessly impractical but it is not! The general approach in algebra has produced powerful new methods for “algebraizing” different parts of mathematics and science, formulating problems which could never have been formulated before, and finding entirely new kinds of solutions.A Book of Abstract Algebra by Charles C. Pinter
Such excursions into pure mathematical fancy have an odd way of running ahead of physical science, providing a theoretical framework to account for facts even before those facts are fully known. This pattern is so characteristic that many mathematicians see themselves as pioneers in a world of possibilities rather than facts. Mathematicians study structure independently of content, and their science is a voyage of exploration through all the kinds of structure and order which the human mind is capable of discerning.