Annotating Serre

I very much like the thought of annotating the book “A course in arithmetic” by Jean-Pierre Serre. It is a fascinating and dense math text book that I find very attractive. The book has also been recommended by Richard Borcherds as one of his favorite math books, and I very much like Borcherds’ online math lectures.

But on the other hand, “A course in arithmetic” is a very hard book. I tried to read parts of it and most of what I read seemed to be very hard to understand. As I wrote in the second sentence: It is a very dense book. And people with much better mathematical backgrounds have tried before me and struggled:

When I read this reddit thread, I could very much sympathize with the original poster. But I was even more fascinated by one of the posts’ linking to this annotated version of the book: It is admittedly not a complete annotation of the book but it is a nice start. It seems to be a project that started in a graduate course at the University of California, Santa Cruz.

Another answer reads like this:

Serre always gives the maximally elegant proof, putting in only what he considers the absolutely necessary steps. No motivation is given. This is the style popularized by Bourbaki. (A French mathematician informed me that they did this because didn’t want to contaminate the reader with their informal mental picture of what was going on. The reasoning was that their teachers would provide the intuition and “picture”).

But to appreciate this elegance and economy of presentation, you either have to be so mathematically gifted as to be able to immediately see why he would do things the way he does, or to work hard and gain experience. (Most of us have to go the latter route).

I think I would like to work through some parts of the book myself and see what annotations I come up with.


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