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This is a question that has been in my mind for a month now. I am a final year M.Sc student in mathematics and applying for graduate school this year. But for applying to graduate schools, let's say in Europe, it is recommended that you should study the papers of Professors to whom you are applying. My question is how to go about reading the papers? Let's say I am interested in doing research on a particular topic (let's say X) and I have only taken a basic course on that topic X. I should have done my M.Sc thesis in X but in my university, nobody is working on X. Also, I didn't know I am interested in X until the last year otherwise I would have done some internships on this topic. With this background, there is no way I could understand the papers of a Professor who is working on the subject X for years. This is certainly not a problem in the US as you don't have to apply to a Professor, but in Europe, I think in most of the cases, you have to directly apply to a Professor. So, what to do in this case?

Thanks in advance! Sorry for my bad English.

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    Being able to read papers is just as important in the U.S. How do you have any idea you are interested in X if you can't read about it?
    – Bryan Krause
    Nov 2 '18 at 17:49
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    @BryanKrause Presumably by having learned about the fundamentals of the subject from textbooks. Being able to actually read a research paper in math is not something one is expected to be able to do until quite a bit into the PhD, and even then only in the somewhat narrow area of ones PhD. Nov 2 '18 at 19:07
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    @TobiasKildetoft Got it. That seems very particular to math, then, and as an outsider seems to me like an incredibly dangerous thing for a field.
    – Bryan Krause
    Nov 2 '18 at 19:10
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    @JessicaB That's kind of my point, though...stuff in other fields can get pretty esoteric, too, but there is an expectation that a given work contains enough to get someone up to speed on terminology if they are at least familiar with the general area. Limiting a subfield to too few people who can understand it seems like a good way to get overly isolated from reality (even mathematical reality..). Particularly if, as your comment elsewhere mentions, it's necessary to go into multiple languages for those terms.
    – Bryan Krause
    Nov 2 '18 at 22:14
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    @BryanKrause - Papers do have enough for someone to get up to speed if they are familiar with the general area. It's just that mathematics has lots and lots of 'general areas', and each of them is very small in terms of number of people. Mathematics as a whole isn't aiming to study one particular thing or kind of thing (a single mathematical reality as it were); it is the practice of making art out of logic, and artistic diversity is a good thing. Nov 3 '18 at 0:12
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Don't expect to understand the whole paper. Many researchers won't manage that either anyway, without a fair amount of time. Read the introduction. That should be written in simpler/less technical words, and give you an idea of what's going on. If that's still too hard, identify the main words in the title/abstract, and see if there are corresponding articles of Wikipedia (which isn't reliable enough to quote, but in many areas is actually pretty accurate).

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First an answer that is (half) joking. Try to read the paper. If that fails your understanding, get the papers cited in the references and try to read those. Proceed recursively deeper until either (a) you understand the paper(s) or (b) you reach Euclid. In case of (b) you should probably find another field. In case of (a) work forward again to the original paper.

While there is some truth to the above, appalling as it sounds, note that the farther you go back the broader is the coverage of the papers, generally speaking. The research frontier (where the professor wrote the paper) is very narrow in mathematics. But it has a lot of background that goes into getting to that frontier. If you understand that background, or at least some of it, you are doing well. The research edge is like the tip of a funnel, with a wider body of knowledge behind it. Textbooks stand a fair ways back from the frontier, but maybe a bit closer to the edge than they are to Euclid. If you have a good general understanding of the broader field (analysis, say, or algebra) you won't have to go back too far.

I'll note that this is much easier to do now than it was fifty years ago. Then, to trace back a chain of citations you had to go to a physical library and for many of the papers ask the librarian to get you a copy from some, yet bigger, library. Now, the more recent stuff is available online, though you may still need to have the librarian get you a copy to avoid charges imposed by publishers.

It is a hard job to get started in this. Having done it once, however, for a narrow field, the outlines of what is known in that sub-domain will become clearer to you and you won't need to repeat this too often. Moreover, the funnel narrows fairly quickly so there is, perhaps, less to understand than you might fear.

In my own case, the number of steps back from the edge to what you could find in good analysis textbooks was only half a dozen steps, if you had the right insights. The essential papers you needed to read to get the insight was, again, only half a dozen or so. With those insights I can explain the essence of my work (very old now) to good undergraduates, though not with all the details. OTOH, it is probably the professor him/herself that will give you those insights.

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    I don't think this would be helpful in my (sub)field. Going back a couple of papers often means you switch into German, or Russian. Or you get back to before suitable terminology existed, or matched what we used today. Euclid might well be the first recognisable thing you find, and that wouldn't be unreasonable for a MSc student.
    – Jessica B
    Nov 2 '18 at 21:37

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