I noticed that if one wants to get into a new branch of mathematics it is really hard to find good literature to start with. Of course, if one googles the name of the subject one will find a 1000 pages book that contains all the established theorems and proofs. But as a start, an informal survey article is probably more helpful. How do I find such articles? Should everyone in each specific case go to their professor or is there a uniform place where one can look for such literature?

I also noticed that one of the main problems one has if one wants to start doing research is that it seems all people involved in the current literature (who write all the new research papers) know all the usual tools that are used to solve problems of a specific kind, and if one wants to start participating there is the feeling that the preknowledge is missing. But this knowledge is maybe only communicated orally from professor to their PhD students, and as an outsider it's hard to find appropriate literature. But if there is, where can I look for it?

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    $\begingroup$ I find google scholar is pretty good for those kinds of searches. Surveys usually come up, but if you don't find a survey you'll find papers covering the subject and you can start going through references. $\endgroup$ – Michael Biro Aug 16 at 15:31
  • $\begingroup$ That's a good suggestion, thank you! $\endgroup$ – user696269 Aug 16 at 15:48
  • $\begingroup$ Usually, said 'informal survey articles' are called review papers. $\endgroup$ – mattos Aug 16 at 16:13
  • $\begingroup$ Search e.g. in Mathscinet. $\endgroup$ – IV_ Aug 16 at 18:35

I think that what you're looking for may be the Princeton Companion to Mathematics. This book provides introductory survey articles, written by experts, covering much of pure mathematics.

According to the publisher:

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more.

The Princeton Companion to Mathematics is definitely where I'd go to get the lay of the land regarding some area of mathematics before delving into more technical articles.

On the other hand, if you're interested in knowing what's being done regarding a more specific topic and what sort of techniques the experts are using, you might find the survey articles in the Bulletin of the American Mathematical Society helpful.

The description of the journal on BAMS' website states:

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic.


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