I'm about to enter a math PhD program at a pretty good school, but the job market for research university professors has been terrible as far as I can remember (since the late 2000s recession). I hear many stories of hundreds of excellent candidates applying for one or two openings.

Older professors tell me it wasn't always like this. What did the market look like when it was considered "good" and could it ever come back by the time I finish in 5-6 years? Or has there been a fundamental shift in academia preventing the good times as we knew it from ever returning?

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    One factor in your favor is that the "baby boom" generation is approaching/entering retirement age. But it may be more like 10 years before this has a noticeable effect on job markets. – user37208 Jul 11 '16 at 22:10
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    Yes, the job market nowadays is not what it once was. On the other hand, if you like spending your days doing math, and don't care about getting rich, academic math is not the stupidest gamble, in the sense that, in the worst-case scenario, you have to get "a real job like everybody else". But, yes, "academic math" is not a "career choice", but more a way of converting a hobby/obsession into something that pays a bit, usually with health insurance. – paul garrett Jul 11 '16 at 22:23
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    And if you have a PhD in math, you should be able to find a fairly interesting "real job" more easily than looking for one with just a bachelor's degree. – Peter Shor Jul 12 '16 at 0:18
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    I wonder how closely this relates to the computer industry job market. Pure speculation, but could it be that people are transitioning into software engineering and the like from "pure math," which almost by definition is unmarketable? (That is, if you define "pure" as "not applied to real-world or business problems.") The computer industry job market isn't hurting that I can tell. – Wildcard Jul 12 '16 at 11:49
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    Maybe in the past, with scarcity of mathematicians, they could follow their passion and find a job. Now you kind of have to find what will be in demand in the futur (big data, ai, ...) and find your passion in that. You need to be a bit smarter in the type of research you'll be doing. – the_lotus Jul 12 '16 at 12:02

First, some historical perspective: Francis Sowerby Macaulay and Hermann Schubert, two mathematicians from the late 19th century whose names you still hear repeatedly these days if you come anywhere near algebraic geometry, both taught high school.

Second, a counting perspective: Research university professors probably average a doctoral student at least every five years, with some averaging more than one a year. This means every professor produces somewhere between 6 to 40 replacements over the course of their career. Assuming no change in the number of jobs, only one of those replacements will get a research university professorship.

Third, a practical perspective: It's hard to imagine research in mathematics, especially but not only pure mathematics, having direct practical benefit to many people. That means the amount of funding purely for research tends to be rather small. Even at research universities, teaching is an important rationale for paying a professor's salary, and the benefits to teaching are an important justification for research.

What happened between the 1950s and 1980s, particularly in the US, was an enormous expansion in higher education along with a massive increase in research funding. The US went from having about 5% of its 20-year-olds going to college to about 50%. Assuming a corresponding increase in the number of professors, this meant a professor could advise 10 PhD students and have every one of them get a job. For obvious reasons, we will never see a 10-fold increase again. Also, the US was enormously wealthy and had resources to spend on less practical purposes like mathematical research and providing high quality university education. (The US still spends about 50% more per university student than Germany. Most of that is going to smaller classes with more attention paid to helping students along.)

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    I would like to contradict you; lots of research in applied mathematics has direct practical benefit, even if the majority of it doesn't. – Peter Shor Jul 12 '16 at 0:21
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    What happened between the 1950s and 1980s, particularly in the US, was an enormous expansion in higher education The other big thing that happened during that time was the conversion of full-time jobs into part-time jobs. That change is never going away. – Ben Crowell Jul 12 '16 at 0:43
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    "It's hard to imagine research in mathematics ... having direct practical benefit to many people." How about RSA (which is based on number theory)? Or digital circuits (from boolean logic)? Or GPS (those working on non-euclidean geometry didn't think space worked that way)? – PyRulez Jul 12 '16 at 2:12
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    @PyRulez - I don't think any of those examples count as "direct". – Alexander Woo Jul 12 '16 at 2:23
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    'That means the amount of funding purely for research tends to be rather small'. No. It is something specific to our current society that funding for research depends on 'direct practical benefits'. There is plenty of scope for funding things with only indirect practical benefits, or direct philosophical or spiritual benefits, or nebulous indirect impractical benefits, but we choose not to make that decision. – jwg Jul 12 '16 at 10:10

Compare page 3 of the AMS annual survey from 1999 with page 4 of the 2008 edition and page 4 of the 2014 edition, in terms of employment for new hires we are actually much better currently than the early 90s.

Depending on the age of the individual you talked to: the good old days could be everything up until the late 80s, when rate of unemployment remain largely below 2%, and new graduates are often immediately hired on tenure-track positions. We are almost certainly not going to return to that level of employment: in the post-WWII era through the cold war there have been (for one reason or another, GI Bill for example) expansions in funding for academia. That growth was never sustainable. As a benchmark for the future you probably want to consider the data from 1990 on.

If you look in the 1999 data, of those obtaining employment in the United States, just under 30% (of the new PhD recipients) are hired in postdoc positions and a bit over 50% in permanent positions (30% in academia and the other 20% in industry/government). The 2008 data is similar. The postdoc percentage is higher in 2014 (38%) but not outrageously so.

You can spend some more time teasing out the data yourself; the annual survey results are available online for the past 15 years, and presumably the AMS has the old data dating back to the 50s available somewhere.

If you want to be more forward looking and consider hiring statistics overall instead of just for new PhDs, since the economic crisis the AMS has been running employment surveys every years. A quick glance at the 2014 survey suggests that things have improved slightly.

As a side remark: the large number of applications mathematics positions receive has in some part to do with the availability of MathJobs.org. The website makes applying to 50-100 positions in one hiring cycle relatively easier in mathematics compared to other academic fields without a similar centralized job database. So the inflation of number of applications received per opening compared to "old days" does not 100% correlate to the health of the job market.

  • Exactly. The GI-Bill-fueled expansion of college populations, and Cold-War-fueled expansion of federal research funding (and rationalizations about teaching loads), has not continued, and would not have made sense to continue. But the general structure and mythologies were/are grounded in that expansionist time... On another hand, in what line of work is everything always easy? The (falsely) "Golden Age" (which was unsustainable and substantially delusional) is over. I must say that I feel lucky to have caught that wave a bit, but even in the best of times academic math required... [cont'd] – paul garrett Jul 11 '16 at 21:57
  • [cont'd] ... personal sacrifices, geographic location very significant among them. Especially prior to "internet", leaving family, friends, and maybe working spouses/partners behind... and more than once? – paul garrett Jul 11 '16 at 22:00
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    @Significance It varies significantly between Universities (rank/popularity and if it's research or teaching focused). Some get well over a hundred applications per position, and some (especially smaller liberal arts and/or little state schools) fail their search because they didn't get enough applicants or no one took their offer. – BrianH Jul 12 '16 at 2:09
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    @Significance: I work at a large public research university. Last year we advertised for one position and got over 400 applications. And I've heard of places with even worse ratios. – Willie Wong Jul 12 '16 at 13:50
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    @Significance: I work at a top-5 math department, and last I heard I believe we got something like 600 postdoc applications. But as you can imagine, the number of serious candidates is much much smaller -- so these statistics, although striking, are ultimately rather uninformative. Most of these applicants are just checking off all the top universities on MathJobs, because after all, why not? (We still read every application, though!) – Tom Church Jul 16 '16 at 6:04

There are different levels of "good". In 1969, as I was starting my last year in graduate school, a senior professor told me about job-hunting: "Well, you should decide where you want to go and assume that we can get you in there." I'd call that a good job market. But, in my case, it didn't work that way; apparently the greatest effects of the post-Sputnik boom in math had just faded away. So did I encounter a bad job market? By comparison with prior years, yes. But I sent out a total of three applications and got two offers. By comparison with more recent times, that was still an extremely good job market. I see no realistic hope for things to get that good again.

  • When someone invents FTL, teleportation or the Ansible, things will pick up again, don't worry. – user28174 Jul 13 '16 at 13:50

In my opinion, there are two factors that define a "good" job market. One of them is NOT how many people apply for any given position. The number of people applying for a position depends on the number of people graduating, the number of people who want to switch universities, and the number of people who want to switch careers. I believe even in a good job market, you can still get 100s of people applying for positions. I do not believe a "good" job market means that everyone who wants a TT position with a 1-1 teaching load (i.e., 1 class in the fall and 1 in the spring) at an R1. I think a good job market means the "top people" (I don't want to define "top people") eventually get a job.

The first factor that I think defines a "good" job market is the number of positions "good" positions being advertised. I think of a "good" position in the US as a TT position with a teaching load less than 3-3 (i.e., 3 classes in the fall and 3 in the spring). My field is on the small side, so in a bad year, there would be less than 5 positions targeted to my specialty and in a good year 10+. In a good year there might also be another 10+ open calls and another 10 or so calls where if you squint enough you can argue you fit. So in a good year there might be 30 or so "good" positions to apply to and in a bad year less than 10.

The second factor is the number of positions that will help you progress. These could be soft money research positions or poorly paid one year visiting positions with a reasonable teaching load with colleagues that will help you become a better researcher. I do not consider 5-5 adjunct positions as helping you progress. Most of these progression positions, at least in my field, are a direct result of grant funding. They could come about from someone on the job market getting a grant themselves or from a current faculty member getting a grant to buy out of their teaching. In a good job market, there needs to be enough of these that the "top" people can avoid being unemployed and stagnating for a year.

  • I think this is a nice answer, but some points don't seem to apply to math. I've never heard of a soft-money research position in math, for example. – Tom Church Jul 16 '16 at 6:06
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    @TomChurch when I wrote the answer, the question was more general than it is now. – StrongBad Jul 16 '16 at 10:37

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