A life of PhD: is it feasible? In the next year I will (hopefully successfully) graduate from a PhD programme in pure mathematics. The location is (continental) Western Europe, the topic of the thesis is arithmetic geometry, if it matters. During my PhD experience I have found out the following things


being a pure math PhD student is a relatively stress-free existence for me. I can just waste all my time learning some math and occasionally writing some papers;
the stipend does suck but I am frugal person from a very poor country so I do not care that much (nor do I have a family to feed);
if I could, I would not mind spending what is left of my life in a PhD programme. In particular, I do not feel any intrinsic motivation to try to get a tenure-track position.


The question is: is it feasible for me to keep applying and getting accepted to pure math PhD programmes before I die or decide to retire? To clarify, I don't really think that I will be a problematic student; during my PhD programme, I got 3 publications accepted in reasonable journals (rank A in AustMS ranking) and I think I could maintain a similar rate of work. 

Are there any "magic words" I could tell the committee that considers the applicants to improve my chances?
Holding a PhD in math would usually disqualify you from being admitted into a PhD program in mathematics. Even if it does not do so officially, I'd consider it next to impossible to get scholarships.

That said, being a postdoc in math is not really much different from being a PhD student. However, even being a postdoc forever is not easy. Many funding sources have restrictions on how long ago your PhD may have been - after 5 years you already have fewer options, and continuing long after 10 years will see you face exclusion from many funding sources, as well as a strong social pressure to get a "proper" job (i.e., a faculty position).