Careers advice for Ph.D.s without current postdocs or university jobs Hi,
I'm sure I'm not the only Ph.D. mathematician on MO in serious need of career advice. I'm sure there will be other readers in similar situations, who will find any good advice very helpful. Can anyone suggest anything? Honest, serious answers only please. 
Note that the obvious advice, i.e. do lots of great research, write loads of papers, make friends with lots of professors at conferences and seminars, apply to many jobs, learn loads of new topics, get a brain upgrade, etc. etc. etc. is already known to me and most other people on MO.

Background motivation
Suppose someone (who shall remain anonymous, but let's call him Dr.H for the sake of argument) is in the following position:
Dr.H has a Ph.D. in Pure Mathematics from a good English university.
Dr.H's Ph.D., whilst perfectly respectable from the mathematician's viewpoint, is not known to be of any use for industrial research or non-university jobs of any kind.
Dr.H has several years' postdoc/lecturing experience, but only at universities with very low academic reputations, which has now ended.
Dr.H has several published papers in good journals; but unfortunately, less than other people of his age in his area. He can do good work, but too slowly.
Dr.H currently has a non-university, non-research job teaching in a school, and cannot easily attend conferences, seminars, university libraries, etc. etc., and consequently Dr.H now has even less time for research than before.
Most advertised mathematical jobs (e.g. www.math-jobs.com, www.jobs.ac.uk), both academic and non-academic, demand teaching experience or other skills which Dr.H does not possess, and does not know how to acquire.
SUMMARY: Dr.H's research record is quite good, but it seems not good enough for Dr.H to get a university job involving research. However, Dr.H's teaching experience also seems not to be good enough to get a purely teaching university job. So Dr.H appears to be in a very tricky situation!

Question: what should Dr.H do?
Does Dr.H have any reasonable chance of continuing his academic career? If so, how? (Apart from the obvious "apply for more jobs, publish more papers").
Should he apply to advertised university jobs, even though he does not satisfy the requirements? Isn't this simply a waste of time?
Or should Dr.H abandon the universities entirely and seek non-university jobs?
Does Dr.H have any real advantage over new B.Sc. Mathematics graduates when applying for non-university jobs of relatively low mathematical content? If so, how should he find such jobs, what exactly are these advantages, and how should he make full use of them?
Important note: in your answers, please state which country you are referring to, since this can make a big difference!
 A: Maybe you should apply for a position at a university in a developing country. 
In Brazil, at least, it is much easier to get a position (few candidates, usually not strong as in European universities). Maybe you should start with a postdoc (you can even have one scholarship from Brazilian government) and think about something next if you adapt yourself to the country. In this case, I think the first step would be contacting a local researcher in your area and discuss the possibilities.
A: I must preface this by saying that I am not a math PhD (though I am intent on becoming one), but I have met several from UC Berkeley and can say that getting a job in industry is not always dependent on specific field of study.
I know someone who was a topologist who got a job at an international bank, with, so far as I know, no training in the area. He did comment that, in his particular case, he felt a bit underused, but I mention this as an example.
At Berkeley they have a career opportunities for math PhDs, and I can attest to the fact that the most pure of mathematicians have taken jobs that are not at all pure in the sense of without application. There was, in fact, one set of three people who all went on to some form of software engineering.
It's not coming up at the moment on my browser but you might check
http://math.berkeley.edu/~urep
They may have posters from previous such sessions. You may be able to get in touch with some of the speakers I don't know, either by finding their email through the google or asking one of the people in urep.
A: To add to many other good, informative answers and comments, I would reiterate a certain maybe-negative-sounding point, that one should not base future plans on one's own research results or other achievements becoming substantially different from what they have been in the past. 
Thus, the "wonderful paper" will most likely not occur, if one has not had too many of these in the past, and "betting the farm" on its occurrence is just stupid, especially if people are depending on you.
This is a special case of predicting that the near future will strongly resemble the near past...
So far as I can tell, loosely based on actual facts, but certainly on substantial direct observation, the extra-academic job market for Ph.D.'d mathematicians is growing faster than the academic job market, which these days grows at most at the rate of population growth, to match undergrad enrollments. The "problem" in academe is that the recent-years' production of Ph.D.'s has grown at a rate exceeding market growth, by a huge factor... this horribly exacerbated by the economic mess of 2007-9, etc., ... but in any case observing that the academic job market (in the U.S. for sure) is over-saturated...
Some of this is a result of lifting mandatory retirement in the U.S., but/and mandatory retirement in Europe seems to motivate some mathematicians in Europe to emigrate to the U.S. to maintain an "active" role, ...
So, unfortunately, if one gets off to a bad start in some way in academe, things are so tight that it's hard to recover... whether or not one could recover "in principle". So, if practical matters dominate, looking at actuarial stuff in the U.S., or banking/finance, could be more practically viable than trying to get postdocs or temporary teaching positions and "stage a comeback". Sadly, perhaps.
A: I am going to give a non-serious answer, but there is a serious point behind.  Lots of current and former mathematicians and theoretical computer scientists excelled in other fields.  Here is my top 10 list: 
1) You can change your name and start selling puzzles.  
2) You can drop out and start a company (this or that, whatever). 
3) You can start a hugely successful hedge fund which will in turn employ over a hundred other Ph.D's.  
4) You can write a popular book explaining why people can't count. 
5) You can write a comic book, a very good one.
6) You can write three volumes of a proposed seven volume monograph, get upset over its print quality, invent a new way, write a manual on it, and sell these and other books in dozens of languages.  
7) You can design a bomb. 
8)  Why stop on a bomb?  You can move to NJ and design a computer.
9)  You can start a company selling in bulk a number-theoretic algorithm accessible to undergraduates.  
10)  In the good old days you could become French Minister of the Interior, but it helps to be friends with an Emperor.  
UPDATE:  while writing I discarded a few other career choices which I felt were somehow "less relevant", such as Iraqi Oil Minister, Russian oligarch, or even World Scrabble Champion.
A: Tell Dr.H to try to start with a short term visiting position (visiting instructor/honorary fellow/etc.) at some "reasonably good" (whatever that means) university. These are much easier to get than regular faculty ones (In many cases all you need is to know somebody who has a grant and is interested in collaborating with you. Such positions do not go through the formal hiring process and can, in fact, be offered by any faculty member: all one would really need is the chairman's approval and some source of money (say, a grant or a startup supported by some small contribution from the department if teaching is also involved). I invited quite a few people this way myself). That won't bring Dr.H high salary or job security but it may give him some extra time in the academic setting. What he makes of that time depends entirely on him. Of course, some "exit strategy" is a must for the case it doesn't work out. I wouldn't advise taking too much risk in the current economic situation with unemployment rates hovering over 10%.
@Greg The advertised level of seniority is not really negotiable and that has nothing to do with the department politics, it is just a legal issue. What you can negotiate though is the early consideration for promotion. 
A: Based on what I read, I would recommend that Dr. H seek a career outside academia. I'd advise Dr. H to seek out, via friends and acquaintances, other math Ph.D.'s who have successfully found careers that they are happy with and learn about their jobs, as well as how they managed to get them. There are not a few companies who have found math Ph.D.'s worth hiring, but you do want to walk into the interview sounding knowledgeable and motivated (i.e. with a positive and confident attitude), even if you don't have much experience. So you might want to devote some time to learning some additional stuff either on your own or in courses. Finance is a popular choice, but there are many others available.
Of course, if Dr. H really, really wants to do academic research and teaching, then I'd advise the greatest possible flexibility in terms of the location, quality, and type of academic institution.
A: One answer is that it is certainly not always a waste of time to apply for a job even if you don't think that you fit the ad.  It's easy to just keep copying your application, even trivial in MathJobs.  Moreover, you should take the details of ads with a grain of salt.  The semantics of research areas are often based on internal department politics.  Who knows what they really mean if they say that they want to hire in "mathematical physics" or "geometry", etc.  Even the advertised level of seniority is sometimes negotiable not an obstruction, because the department can consider workarounds such as early promotion.  (Corrected at fedja's suggestion; I didn't mean that it was "negotiable" in the direct sense.)
Another answer is that, for the sake of your sanity, you should have a "Plan B" if you want a tenure-track research job in mathematics.  It is not so difficult to major in mathematics, but after that the available positions from graduate school, to postdocs, to tenure-track research positions are a severe pyramid at every stage.  Then, two-body problems can make things even more difficult.  The two basic choices for a Plan B are industry and teaching, and you have to decide which one is more livable for you.
In my case, it would have been industry.  It is true that it takes new skills to have a career in industry, almost always involving computer programming, and sometimes also statistics and applied math.  But it is not necessarily all that formidable.  If you can get past the personnel office, many managers realize that mathematicians are fairly adaptable to new skills.
Likewise, teaching is not necessarily all that limiting; many people with teaching positions find ways to have good access to the research community.  A few even get good research positions at a later stage.  But if "Dr. H" is not at peace with this type of "Plan B", then maybe he should consider the other type.
For both answers, my experience is in the United States.  That said, an important answer for all countries is to expand your geographical range as much as possible.  Going by the obvious statistical calculation, it can make a huge difference.  When my wife and I were on the job market, we applied all over the US.  Although we're happy where we are, we could have given more consideration to the rest of the English-speaking world, certainly Canada but also even places like Singapore.

Also, since the question seemed to steer away from it, I didn't say anything above about  the mechanics of "obvious" methods.  However, here is one thought that may not be so obvious.  There are more effective and less effective methods for getting visibility as a research mathematician, and for that purpose the Web is a new world.  It makes a big difference if someone on the search committee knows your name before they see your application.  Of course, it's obvious to just try to "be visible" by writing papers, giving talks, and meeting people.  What's not so obvious is that it can help a lot if you make effective but judicious use of new tools:  A good home page, the arXiv, and now MathOverflow.  Of course you shouldn't semi-spam the arXiv or MathOverflow --- that will lead to bad consequences.  But if you use them properly, they can be more effective, and differently effective, than giving talks at this or that meeting.  By contrast, e-mail during job season is one of the more obvious steps, and I have to say that that tactic is overused.
A: Become EPSRC program manager and show your former advisor who the boss is :-))
Other opportunities involve


*

*administrative or purely teaching jobs at universities,

*teaching Maths in a private school, -

*jobs in academic publishing,

*research jobs in industry (IT, petrochemical, pharmaceutical),

*spying (GSHC or KGB - have you heard of Anna Chapman?),

*law conversion (solicitors specializing in IP),

*other businesses (actuarial, treasury, accounting - requires a training contract).

A: This answer is related to fedja's.  Many universities, at least in the U.S., hire various kinds of adjunct faculty to help with the departmental teaching load.  (These positions are often called "visiting professorships", but I don't have in mind the kind of short-term research visiting collaboration that fedja discusses, but rather semester or year long positions, funded by the dept., not an individual, for the primary purpose of helping with the teaching needs of the dept.  At least at my university, these are not offered by individuals; very likely the details of how they are offered differs from one dept. to another.)
At my university, and I would imagine at others, the basis for the offering of these positions is quality of teaching.  
Obtaining such a position, and doing well at it (so that one gets subsequent strong teaching recommendations) can be a foot in the door to a teaching-based academic position.  
Also, at my university (and I know we are not unique in this, although perhaps uncommon) there are no math classes taught in lectures of 200; everything is taught in classes of around 30 or fewer students.  So what matters is the quality of the teaching recommendation in relation to teaching such classes.   Speaking more generally (and so less authoritatively), I would imagine that for teaching recommendations in general, the quality and strength of the recommendation is important (the applicant should have a record of good lecturing skills, sincere relationships with students, etc.) rather than the precise nature of the previous teaching experience.  (After all, some new Ph.D.s will be hired to positions in which they might have to give 200 person lectures, but even if they have had prior teaching experience as a grad student, it is less likely that they will have given lectures to a class of 200.) 
A: I am more or less in the same situation as you are. After careful consideration I decided that I should abandon academia for good. Because as far as I have seen your career in academia is very dependent on where you start out. If you do a postdoc in University of Nowhere the chances of getting a decent job after that will be even lower than it is now. There is a temptation to think that by hard work you can compensate for the bad start in your career, resist that temptation.
As it stands now I will be applying for finance jobs later in summer. Consider applying to big traditional banks (J P Morgan, Chase Manhattan, Wells Fargo, ...) investment banks (Goldman-Sachs, Morgan Stanley) and big hedge funds (Renaissance Technologies, D E Shaw, Citadel). If you want more info about 2.5 years ago there was a small article in Notices on the transition from academia (specifically math) to finance. The author had a Ph.D. in number theory and went on working for D E Shaw (PDF): http://www.ams.org/notices/200806/tx080600700p.pdf 
Also don't worry about the state of financial firms. They have fully recovered from the effects of the great recession of 2007-2009: http://motherjones.com/kevin-drum/2011/03/chart-day-finance-back 
A: I was in a similar position.  Short answer get some skills the market requires. 
A PHD in maths from a decent university, you should waltz into quite a few jobs. I would try science areas, Cambridge, Oxford, London, and maybe the field of bioinformatics (lots of statistics obviously, and lots of recruiters).
Get a decent recruitment agent. Practice coding.
Have you tried contracting/consulting in London, do you know matlab ?  
I have assumed yr in the UK (apologies if not). There are positions out there for good candidates.
A: Do you think you have "three year's research experience outside of the EU"?  If so, you could look at a Marie Curie International Reintegration Grants: http://cordis.europa.eu/fp7/mariecurieactions/irg_en.html  Fortunately the deadline is September; you'd need to find somewhere in the EU to support your application (such a grant doesn't bring overheads, so people won't be falling over themselves to host you, but it does pay salary etc.)
Marie Curie grants are competitive, but I think are a little less competitive than some national based grants.
A: I feel for Dr. H. It must be frustrating not to find an outlet for the passion that we mathematicians all possess in such large measures.
However, Dr. H need not lose hope.  There are several areas outside of academia where there is enormous mathematical activity; I'd like to point Dr. H to two of these.  The first is communication, particularly wireless communication.  There is a tremendous amount of mathematics in this field, and importantly, a large number of unsolved problems of an intrinsically mathematical nature.  Companies ranging from the very large (e.g., Nokia in Europe, Qualcomm in the US) to the very small (startups) would be very interested in hiring people with mathematical skills. It would take some preparation, but with advance research on what is needed and with commitment, it can be done.  (Perhaps one can look for an internship while learning about the field.)
At the risk of appearing to put in a plug for one's own work (sorry!), I'd like to point Dr. H to a survey article I wrote on some mathematical problems in wireless communication, which he may find instructive:  Division Algebras and Wireless Communication 
The second area is "national security."  (Disclaimer: I myself am very uncomfortable with this whole subculture, and would not go there unless there are very compelling and pressing reasons truly connected with security, but Dr. H may have a different world-view.)  At least in the US, the national security apparatus appears to be a major locus of mathematics.  Besides the head office ("NSA"), there are two think-tanks, one in Princeton and one in San Deigo, that hire large numbers of mathematicians, and, I am told, put them to work on quite interesting projects.  Of course, no one on the outside really knows what goes on there (to quote one of those on the inside: "I could tell you, but then I would have to shoot you!"), but at least at these two think-tanks, they give you a basket of problems and ask you to work on whichever you like, and in addition, they do give you time to do your own mathematical research.  The UK may have similar programs, perhaps Dr. H may want to explore.
A: The academic job market, at least in the US, shows no signs of improving.  I would suggest at least considering non-academic positions.  In my experience, the exact field of the mathematics Ph.D. is less important than attitude and flexibility in considering alternatives.
For specific ideas, SIAM provides a couple of good websites:
http://www.siam.org/careers/thinking/work.php

http://www.siam.org/careers/thinking/organizations.php

Although these tend to focus on the US, I think comparable opportunities exist in the UK as well.
Bill Satzer
