I have completed a 4 year bachelor of Mathematics at a decent university, and a comment was made by Pete L. Clark, on this website, here: "post-PhD academic job market is one step shy of airtight at the moment."
I was intending to study a PhD in america, and am wondering if his statement rings true in the most part. Is it truly difficult to find a post-PhD academic job, specifically in Mathematics, and if so, are there relevant statistics backing this up?
The American Mathematical Society publishes detailed data about mathematics employment in the United States. In particular, the Report on New Doctoral Recipients has
"... information about the fall employment plans of doctoral recipients, a demographic profile summarizing characteristics of citizenship status, gender, and racial/ethnic group, the starting salaries, and other employment information about new doctoral recipients"
The data is always delayed by a year because of response and processing time. The most recent report as I write this is 2013-2014. My own take is as follows.
First, the statistics show that the overall unemployment rate is low: a new math PhD recipient is likely to be able to find a job of some sort immediately after graduation. In 2013-14, 85% of math PhD recipients were known to be employed immediately after graduation, and only 5% were known to still be looking (9% were unknown). This is partially due to the ability of mathematics PhDs to look for jobs in business, industry, and government, although the majority work in academia.
Second, based on my personal opinion and experience, the job market for postdocs and research-intensive tenure track positions is very competitive (this is true both in the U.S. and Europe, as well as some other countries and regions). You will need to be one of the very strongest candidates in your area to have a reasonable chance at such jobs.
Third, the market for tenure-track positions at non-research-intensive colleges is also competitive, but in a different way. For these, you want to have a strong vita showing teaching skill and research ability in line with the institution where you are applying. Simply having a PhD and teaching a handful of classes as an graduate student is unlikely to make you stand out from the other applicants.
Overall, because the job market is competitive, if you do enter a PhD program, you need to plan early for the career path you wish to follow. Simply "getting a PhD", and only worrying about the job market in your last semester, is not a good strategy. You want to begin shaping your vita early in your graduate program so that you are in a good position when you graduate.
This varies wildly depending on many factors, from what type of job you want, where you get your PhD, number of publications you obtain, quality of PhD, who your advisor is, and what field you're working in. Any or all of these can and will drastically change the answer to this question and decide if the job market is airtight or swung right open for you.
The academic job market is very difficult, but not impossible. You end up at the end applying to a number of jobs somewhere in the triple digits and you can end up with something from a >10% rate in getting shortlists to none at all. A good way to view this is to ask at the beginning of your PhD for the placement records for their recently graduated PhD students. The graduate secretary should have a list and be able to tell you how students have done in the past. This can be a guideline and tell you how well you need to perform to get the type of job you want. It's also important to note who their advisor is and what field they studied. Look at the placement of the students who graduated with who you may want to work with, in the case that you know that.
One thing to be clear about is that post PhD, even if you do not get an academic job, there is a ton of industry options out there. I applied for three industry jobs when I graduated and got one campus interview that I cancelled when I got an academic offer. There is headhunting for math PhDs to join industry (from both the finance and tech industry). Even if you get unlucky with the market or in grad school, then there are plenty of other options.
