I am a Ph.D. student in mathematics, and I'm supposed to finish this year. I've been looking for a position next year (not so much in the USA, but mainly in Germany and the UK). While I haven't exhausted all my options, I do feel that maybe it would be a good idea to have a backup plan.
Since I can afford it, I was thinking about taking myself somewhere "productive" and living there off my savings for a year, whilst working with the research group in that university to produce new results. In the meantime, to continue to apply to positions and hope for the best.
My advisor said that this is not a very good idea, but at the same time mentioned one or two people from our field who had done something like that (albeit in the 1970s or 1980s).
How bad of an idea is this? And what sort of strategy I should be considering if I want to move forward with a plan like that?
The alternative, of course, is to go out to the industry for a year or two until I find a position. But leaving and coming back seems like an even worse idea to me.
(I have money for a year in a reasonable place, maybe two if I also work a bit during that time. I also don't have an American, Canadian, British or European citizenship; although my passport is versatile enough that I can move around.)
Clarification. While the question is somewhat general, my field is mathematics. I don't think that not having an affiliation will cause me to be inaccessible to my current network of peers. I have seen several people who did not have an affiliation with any mathematical establishment, but nevertheless continued to collaborate with professors, students and all in all conduct interesting research.
As far as my personal case goes, I also don't think there are others from my field of research who got the positions "and might feel nervous if I'm around". More than implausible, it sounds unlikely.