I'm really enjoying the AMS column "What is ..." (http://arminstraub.com/math/what-is-column) and The Princeton Companion to Mathematics.

I am looking for something similar. I'd like to acquire some intuition behind different subjects and the general overview rather than digging into details and technical proofs.

I want to read more about the motivation, the greatest results and applications (inside and outside of mathematics).


closed as too broad by Andy Putman, YCor, Noah Schweber, Johannes Hahn, Piotr Hajlasz Jun 13 '18 at 0:20

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    $\begingroup$ As previous vague and broad big-list questions, this will soon be closed, then reopened, then closed again, then reopened again, ... for some random outcome. $\endgroup$ – YCor Jun 12 '18 at 15:53
  • $\begingroup$ I read through the Bulletin of the AMS, which is a mix of feature articles and book reviews. It's higher level than is ideal for your purposes, but it has given me some idea what's happening in different areas. $\endgroup$ – arsmath Jun 12 '18 at 17:23
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    $\begingroup$ I'll be interested in any answer to this question, but I do think it's far too broad for this specific site. $\endgroup$ – Noah Schweber Jun 12 '18 at 18:04
  • $\begingroup$ "The Princeton Companion to Mathematics" might be a good source for some such material. $\endgroup$ – Michael Greinecker Jun 13 '18 at 2:48

On the popular level, there is an AMS feature column: http://www.ams.org/samplings/feature-column/fc-current.cgi and a series of 10 volumes "What's happening in mathematical sciences": https://bookstore.ams.org/HAPPENING, also by AMS.

On a higher level, there are journals which publish surveys, addressed to the general audience of mathematicians: Bulletin of the AMS, Russian Math Surveys, Sugaku expositions, Gazette des Mathematiciens, Expositiones Mathematicae, L’Enseignement Mathématique, and several other such journals.


An addendum to Alexandre's answer: I have noticed that in some "proceedings" or "conference" volumes, the first article (or the introduction) is a very nice overview of the theory that is treated in the book. The same can be found in books with the title "on the occasion of the [age]-th birthday of [some big name in mathematics]".


Look for books with the word "Handbook" in the title. These often contain well-written survey articles by leading experts. The downside is that "Handbooks" tend to be rather expensive, but you may be able to find them in your library.


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