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I'm going to be a first year graduate student in mathematics and is thinking about which field to specialized in. Besides the important factors such as potential advisor I can find, personal interest, and my background knowledge I want to know the academic job prospective after graduation.

I take a look at recent AMS survey, for example, AMS survey 2012-2013, and for each field of thesis I sum the number of first 8 row("Math Public Large" to "Biostatistics") and divide the number by "Total" to estimate the chance of random Ph.D. in that field get an academic postdoc(in US). I'm slightly worry about the fields I'm interested in have relatively low ratio on this.

My question is, do I interpret the data correctly? If so, how much weight should I put into these data when determining field of specialization? If not, what should I look for?

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Academic job prospects are an important consideration, but the AMS survey results are too coarse-grained for that. They average together people from very different circumstances, which means they aren't representative of any individual job applicant. Some people have much better chances that one would guess from these numbers, while others have much worse chances.

Instead, I'd recommend estimating your chances based on your advisor's previous students and others who have graduated recently from your department. These are both much more highly correlated with your own chances than your broad subfield is. You could view the subfield as a lower-order correction factor, but I'm not convinced it really matters (I'd bet it disappears in the noise). I'd also recommend having a detailed discussion with your advisor about the job market and how to position yourself to do well.

Aside from averaging together students at many different sorts of departments, the field-based numbers conflate several issues: how many people were forced to take a nonacademic job unwillingly, how many people chose one over academic offers, and how many people never particularly wanted to work in academia in the first place. These are all correlated with the field, sometimes obviously (e.g., statistics) and sometimes less so. For example, my impression is that some fields are more likely to attract unambitious students who aren't really on track for academic jobs. I don't have any statistical evidence for this, but I think such students are more likely to choose algebra than geometry, say, because they probably took an algebra course but not a geometry course in their undergraduate studies. If you aren't one of these students, then their existence says nothing about your chances.

In any case, the take-home message is that it's difficult or impossible to extract useful predictions for your own case from this data.

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