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.
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!