I, Samir Siksek, have the immense pleasure of introducing you to three heroes of abstract algebra: groups, rings, and fields. I am not an algebraist. I have nothing but love, admiration, and enthusiasm for the subject. Some of my best friends are algebraists.
Abstract algebra is about patterns. You see one pattern repeating itself across mathematics, and you try to extract the essential elements of that pattern and turn them into a definition. This process gives you groups, rings, fields, vector spaces, etc. You then study and become familiar with each of these new algebraic objects. After that, when you spot one of these patterns in a new context, you’ll say, ‘Aha! I know what that is and what to do with it.
