In [an article][1] written a few years ago, Jean-Pierre Bourguignon estimates that there are around 80 000 mathematicians worldwide, with the AMS having about 15 000 members.  

For France he says 4000 work in academia ("a reliable estimate") and about 2000 in the private sector. Since there are about 60 million inhabitants there, that's 1 mathematician per 10 000 inhabitants.

  [1]: http://smf4.emath.fr/en/Publications/ExplosionDesMathematiques/pdf_en/smf-smai_explo-maths_92-97_en.pdf