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I am trying to come to terms with a variety of new fields as I start doing mathematics research. Often I come across a paper and am lost as to what it's contribution (or perhaps significance is). I do not mean that I think it is unimportant, but rather I don't understand the 'lay of the land' in that field.

What I would like to know is where would be the most appropriate place to get some feedback on particular papers? The department I am in is small and I don't have a lot of direct contact with other Mathematicians, so online somewhere seems like the best bet.

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Mathscinet has reviews of certain papers. –  Eugene Jun 27 '12 at 6:32
A lot of papers don't have much significance. The better writers will write an introduction to place the results in context. If the author hasn't done that, you can always try writing the author with your questions. –  Gerry Myerson Jun 27 '12 at 6:34
maybe mathoverflow? after all it's a q&a forum for research level mathematics, which seems to be what you need... please correct me, if i'm wrong. –  begeistzwerst Jun 27 '12 at 8:22
Many of us (yours truly included) will only be truly honest about our evaluations when speaking in person (so no paper trail :-)) to someone we know well. For important papers that is not such a big deal. But I for one would never tell 'thebigdog' on 'teh internetz' that a certain paper is horse manure. You should also keep that in mind when you read review articles. Few people are willing to be as direct as Truesdell. –  Willie Wong Jun 27 '12 at 8:36
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up vote 5 down vote accepted

Ideally, the reviews in Zentralblatt and MathReviews should provide precisely this information. In practice, many of the reviews are not exactly illuminating. The most important papers, however, often end up getting a "Featured Review" on MathSciNet, and those are usually very clear and well written.

Now, one other way of learning about the significance of papers (if either the paper itself does not provide sufficient introduction so Gerry's advice is hard to follow, or if for some reason you prefer to seek out third-party evaluation of the paper) is to follow the citation trail. Go to the MathSciNet entry for the corresponding paper. On the top right there is a box listing citations to that paper (these are reasonably complete for papers published within the last 40 years). If there are Review articles citing that paper, go and read it. You will likely be enlightened, since the articles will probably also give a good overview of the "lay of the land" so to speak. Citations from references are a bit more hit and miss: sometimes the paper is only cited for a minor technical fact, sometimes the paper is only cited to be polite, but sometimes you will find another paper in the field with a good expository account of why precisely the methods and results of the paper you are interested in is useful.

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Thanks Willie, this is helpful. Actually, following a citation trouble is what got me in trouble in the first place, but I had admittedly been less focused on review articles. Now I've just got to deal with the fact that review articles in Math sometime use the concept of 'introduction to' in the same way graduate textbooks do! –  thebigdog Jun 27 '12 at 21:24
I'd just like to add: The specific paper I was looking for did indeed have a review on MathSciNet, but it seemed to suffer from the err 'lack of frankness' phenomenon you warned me about. –  thebigdog Jun 27 '12 at 21:58
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