I read two comments of Lang that basically places algebra over other math subjects. One of this comments is on his calculus book preface (see Remark 1 below); I am not finding his other comment, but it was an interaction he had with someone at Yale´s math department coffee break and is written somewhere. It basically says that algebra is superior to any other math subject, if I recall it correctly. My problem with his comments is that I have no idea what he is talking about. They baffle me. I suppose I stand in the exact opposite from his viewpoints. For me, you can´t compare the applicability and importance of analysis and differential equations to that of modern algebra. Hence:
1) Is there an article of Lang explaining in detail his viewpoints? 2) or, do you know what is his point?
Remark 1) On the preface of his Calculus book, Serge Lang basically says that he thinks bright students may benefit more in studying abstract algebra before or at the same time they learn calculus. My book is in portuguese, so I give a rough translation: " when I was a student I didn´t like calculus nor analysis. I probably woundn´t like this book either... [today I think] that calculus and analysis are overestimated, with a loss to algebra, mainly because of historical accidents." He goes on to say that a beginner course in algebra should consist in a study of vector spaces and groups, that this is independent of calculus and has important applications to other fields, and that some people prefer this material over calculus. He also says that there is no reason someone should be forced to study calculus before algebra. This being true specially for the most talented students.
Remrak 2) "I remember one time when I was a grad student, I was standing next to him at tea while he was explaining to a first-year that analysis is just “number theory at infinity”. I said Come on, that’s not true. He immediately turned up the volume, challenging me to stop bullshitting and give an example. I said OK, p-adic analysis, and then walked away. But I’ve always wished I had stayed to see what his reaction would have been. We need more trouble makers like him. ", from the site Not Even Wrong.