[注：下文是邮件笔记，内容是早先博文*的摘录，由人工智能翻译。]

"Initially, these organizations were introduced to address problems, serving as tools and in an auxiliary status. It was only later that the focus shifted to studying the organizations themselves - in a word, abstract algebra is the study of the 'organization' itself." (I argued that the layman's term of 'organization' is a better term to replace 'structure'). 

"Having a rough but accurate point of view is greatly beneficial for grasping things on a macro level, so when encountering specific situations, one doesn't feel 'abrupt'."

"In my sophomore year, I once raised a question about mathematics itself (What is Mathematics?), feeling that many university math professors never ponder over such questions."

"There is a book with the same title 'What is Mathematics?', but I do not appreciate that exhaustive enumerative exploration, especially since I am not fond of reading and don't have that much time. The title of this book is universal, but its content, at best, is the authors' exploration, not universal; particularly, it barely touches on algebra."

"I suddenly realized why 'ideal' in algebra is called 'ideal': By extracting a faction A from an organization S, then SA constitutes an (left) 'ideal' of S - each member in the faction and the collective action of the organization can be fully achieved within this 'ideal'."

"An 'ideal mathematician' can freely enter any field of mathematics."