Xjyuk

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 manyn funding sources, as well as a strong social pressure to get a "proper" job (ie a faculty position).

In the U.S. at least, maybe also Canada and Western Europe, in science (math, physics, chemistry, etc.), contrary to legend, graduate school can be a very wonderful, low-stress, idealistic time of life, if one has no partner, no children, no mortgage, no car payments... to worry about, and simple tastes.

On one hand, yes, in some ways grad students are exploited by The System (low pay), but, on the other hand, there is a short-term (5-year!?!) job security, interesting work, and no increase in (student-loan?) debt. And grad students are not terribly experience teachers nor researchers, so there is some kind of quid-pro-quo apart from the low salary.

At my university, it is possible to maintain that lifestyle and employment style by being a "teaching specialist": low pay forever, substantive uncertainty about employment from term to term, but very low stress/responsibilities otherwise. Some people do apparently deliberately choose such a lifestyle. Why not?

But, as @Karl mentions, if nothing else, what about planning for old age? Low pay-ins to pensions (and/or Social Security in the U.S., apart from other complications) will result in low pension payouts later.

Part of the point here is that aiming at "postdoc in perpetuity" almost universally at best would collapse back to "getting paid like a grad student, with no security, no pension". In particular, not getting paid nearly as well as post-docs, in any case.

So it's not that it's impossible to have that lifestyle, but that there are details and complications that would almost surely make you very unhappy later, without any option to go back in time and change things.

(And, yes, I'm sympathetic to your impulse, not being very materialistic myself, etc., but the realities of aging (not to mention having a partner and kids or other dependents, possibly including one's own parents at some point) have long ago burst that bubble for me.)