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Suppose you are a mathematics student who has just graduated and you haven't yet come to graduate school, or maybe you are in your first year of graduate school. Which magazines should you read? I mean general interest magazines, not journals of a specific field, but the kind of magazine that in each volume contain at least a couple of articles that every mathematician could understand (or reasonably try to understand) and be interested in. I don't even know how to describe exactly what I mean. That's why I am asking.

Please post one suggestion per answer.

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I think this should be community wiki. –  Kim Greene Nov 10 '09 at 3:38
    
I've converted this question to wiki. In the future, please make questions like this community wiki; see mathoverflow.net/faq#communitywiki for guidelines on deciding whether a question should be community wiki. –  Anton Geraschenko Nov 10 '09 at 4:08
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For what it's worth, I've learned much more from math blogs than from math magazines. –  Qiaochu Yuan Nov 10 '09 at 5:10

12 Answers 12

up vote 15 down vote accepted

Collected answers from Kim Greene and one from Gerald Edgar:

  1. I hear Mathematical Intelligencer is good but I have never read it.

  2. I have heard that reading things that you don't completely understand is good for mathematicians so I also recommend the Notices of the AMS.

  3. Plus is a math themed magazine. I feel doubtful it would prepare you for graduate school in any way.

  4. College Mathematics Journal

  5. Mathematics Magazine

  6. American Mathematical Monthly

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Gerald provided three. I split his into three to comply with one answer. This made them look like mine. –  Kim Greene Nov 10 '09 at 16:19

I would get a copy of the Princeton Companion to Mathematics and read two or three articles a month.

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I collected Kim Greene's answers into one, which unfortunately makes it look like the answer came from me. (They are fine answers, just not mine.) My own answer is that in Kim's list, only the Notices and the Intelligencer provide a good graduate/professional perspective on mathematics. However, those two aside, the "magazines" that you read should also include the four best Internet resources for serious mathematics: The arXiv, MathSciNet, Wikipedia, and now this site. There are other fine math web sites out there, but as far as I know, nothing else is as important as these four.

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I don't really get how to "use" MathSciNet. How do you use it? –  Konrad Voelkel Nov 11 '09 at 16:52
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Well, you need access throgh a university subscription. After that, it's a lot like Google Scholar, except that it is much better organized. On the negative side, you only search the reviews and not the full text; but the reviews are a great set of third-party abstracts. –  Greg Kuperberg Nov 11 '09 at 17:38
    
So you use it to search for a specific paper or for the latest articles in a journal you like or to get all articles about a specific topic...? Really, I always used Google Scholar to get specific papers referenced elsewhere, where I wanted to get the full text, not just a review. –  Konrad Voelkel Nov 11 '09 at 22:25
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MathSciNet usually has a link to the full text of the paper, it's just that that isn't usually keyworded. Yes, I use it more-or-less like Google Scholar. The main advantage is that the reviews can be enlightening in their own right, and they are sometimes a better source of keywords than the full text. –  Greg Kuperberg Nov 11 '09 at 23:10

I hear Mathematical Intelligencer is good but I have never read it.

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I have been out of graduate school for some years, but I still read this. –  Gerald Edgar Nov 10 '09 at 13:45

I like to look in 'Bulletin of the AMS', 'Russian mathematical surveys', Asterisque, 'Inventiones Mathematicae'and 'Expositiones mathematicae' for articles to read. But mostly I browse the arxiv and homepages of mathematicians, seminars etc.

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Since no one has mentioned it yet, I would like to add the Newsletter of the European Mathematical Society

This is convenient, being online and without subscription, and it has some interesting articles. For example, the last issue has an obituary of V.I. Arnold, and interviews with Fields Medallists Elon Lindenstrauss, Ngo Bao Chau, Stanislav Smirnov, and Cedric Villani.

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Plus is a math themed magazine. I feel doubtful it would prepare you for graduate school in any way.

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Mathematics Magazine

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American Mathematical Monthly

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To add to the list, Nieuw Archief voor Wiskunde is mostly in Dutch, but has a fair number of nice articles in English. They also have a problem section.

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For those who read Russian, there also is Математическое просвещение, freely available online at mccme.ru/free-books/matpros.html –  Sergey Melikhov Feb 20 '11 at 13:44

Students in applied mathematics should definitely make a point of joining SIAM (graduate students can join for free if their institution is a SIAM institutional member), and reading SIAM Review.

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