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I've heard that the trendiness of your area of work is one of the important factor that has am impact your chances of getting job in academia. How far is this true?

Also, how do I decide what areas are trendy and what areas are not in the field I'm interested that is mathematics?

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    One problem with being trendy is that what is trendy now is not the same thing as what will be trendy in the future. At the start of your PhD you might be 10+ years away from "getting a job" – StrongBad May 20 '13 at 8:19
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Trendiness can be factor, but a much more important factor is what needs the hiring department has. If they're chock full of topologists, it doesn't matter how "trendy" your work in topology is: there's a good chance they might be looking to expand in other areas.

OTOH, if they're looking in your area, then being at the cutting edge can't hurt. The danger of course is timing: trends rise and fall quickly, and what might be trendy right now might not be so in a year or two (maybe in mathematics, trends move more slowly).

So I'd argue that trendiness, while one potential factor, is not a universal key factor at all. Every department has their own needs.

As regards your second question, usual measures of "trendiness" include the relative frequency of publication in that subarea. In CS, it's relatively easy to determine this via conference acceptances, but in math I'm not sure how you'd go about measuring this frequency. It also helps to attend big meetings and listen to where the buzz is. An advisor can also be helpful in this regard (especially if they're pre-tenure and need to keep track of trends themselves :))

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    To piggy back a bit off of this, if you actually follow job listings that might be a good way to identify trendy fields, at least in terms of areas of expertise depts. want to hire! Also I would note there are some schools in the social sciences that specialize in particular areas, and so even if they are chock full of people in that area already they are frequently open to more (tends to be good schools, but not the top schools in my field, so their "hook" is some specific area of expertise). – Andy W May 20 '13 at 13:13
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Regarding the third point of Anonymous's suggestion, here's an article Topical Bias in Generalist Mathematics Journals by Joseph F. Grcar in the december 2010 issue of the Notices of the American Mathematical Society.

In many branches of mathematics, the so-called "generalist" journals are perceived more prestigious and publish many of the best results. Typically they claim that they publish papers of the highest quality in all branches of mathematics. However, they don't necessarily accept papers from each field equally likely. In fact, as the linked article's figures clearly suggest, there are clear biases for/against certain branches if you count the papers of a certain topic published in generalist journals and compare the number with the total number of papers of the same kind.

Since good generalist journals are among the most prestigious publication venues in many branches of mathematics, by looking at statistics like this, you may be able to detect prejudices about branches among mathematicians, which is mentioned in the linked article. So, if your definition of "trendy" is highly correlated with this type of prejudice (which I think it is because, all else being equal, the number of publications in prestigious journals in your CV increases your chance of getting a job in academia), it can be a fairly reliable measure of trendiness.

The Annals of Mathematics Anonymous mentioned is definitely among the very top generalist journals. So checking the latest issues may tell you something about what's hot in mathematics now.

The big caveat, however, is that it only publishes 50 or so articles in each year. So, if you only look up in recent issues, your statistics can't be extremely reliable. Using a record of several years defies the purpose of knowing what's trendy right now, so you're in a bit of a conundrum. Making things more complicated, each generalist journal has their own bias as well; different journals tend to publish papers of different topics more frequently.

So, it might be better to take samples from multiple generalist journals which are considered among the top journals by many. Those journals typically publish an extremely small number of papers though. For example, the Journal of the American Mathematical Society published only 32 papers in 2011 (and 35 in 2010) according to ISI Web of Knowledge. Some prestigious generalist journals publish even fewer papers. (I'm not going to talk about which journals you should use for this purpose because it's inevitably controversial and subjective.)

In any case, if you want to check what kind of topic is discussed in a given journal, you can do that quite easily by MathSciNet. The American Mathematical Society classified branches of mathematics and gave a code number to each branch. And they've been keeping track of publications in mathematics. Just search for the MSC code of your field with a specific journal in MathSciNet and see how many hits it returns. This way, you can see how trendy your field is as well as which prestigious generalist journal likes your kind of mathematics more.

This method doesn't always work equally well though, e.g., if you're interested in applied mathematics or mathematical sides of computer science, what the Annals of Mathematics loves nowadays may not be the most reliable measure that reflects what's trendy right now. Another example is when your field became fashionable relatively recently so there isn't a good catch-all MSC code yet. For instance, arithmetic combinatorics has seen a miraculous revival in recent years in mathematics. Ann. of Math. and other prestigious journals are publishing papers in this field, but there isn't a good MSC code to capture this.

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I would recommend that you work in an area of mathematics where big theorems are currently being proven. That usually means that lots of moderate theorems are also being proven.

Some ways to see what these areas are:

  • Go to national conferences; for example attend the (US) Joint Math Meetings and go to the hour-long invited talks.
  • Go to your department colloquium every week, if you have one.
  • Browse through the tables of contents for recent issues of the Annals of Mathematics, and see what areas are getting lots of papers published. (This is a sign not only that these areas are "trendy", but also that they're seeing significant ongoing progress.)
  • Look at colloquium schedules for top-10 institutions, and/or institutions similar to where you hope to get hired. See what kinds of topics the speakers are lecturing about, i.e., what kinds of topics the professors there want to learn about.
  • Browse the Math Jobs Wiki, click through to the web pages of successful job candidates, and skim their papers.
  • (The most important) If you are in grad school, and have not yet chosen an advisor, find out whose students have gotten jobs similar to what you hope to get, and/or are doing interesting work now.
  • Thanks for the reply! I interested in Algebraic Number theory ,arithmetic geometry and things related to that. Will you consider it trendy? – user774025 May 20 '13 at 6:56
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    Yes, very much so. – Anonymous May 20 '13 at 10:06

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