Asking for an extension for decision for PhD offer. And masters vs PhD? I feel in a slightly difficult situation. I have just finished a masters course in pure mathematics, having done a BA in physics prior to that. Both of these were at the institution that is widely regarded as the best in my country- and maybe the world- for mathematics. I applied for PhD programs in my area of interest, and had two positive responses:


University A, probably the best department in my country for my chosen speciality. They didn;t want to offer me a PhD, but I had a personal follow up from one of my interviewers suggesting that my application bes transferred to a second masters course. This course has a high dissertation component, so I would likely be working closely with people in the department. I received an offer for this course, but have not found out if I have funding for it.
University B, probably the third best department in this speciality in my country. They are focused on  only one subarea of this area of math, but are very good at that. Also, I happen to be interested in one other, quite dissimilar area of math. I like these areas both in equal measure, and univesity B offered me cosupervision so that I could work in either area. The proposed supervisors' interests in this second area aren't so closely matched with mine, but I would probably have enough flexibility to work on something more specific to my interest.


Now university B offered me a full scholarship, only 2 working days after I had my interview. But they only gave me a week to respond. I have not heard back from university A if I have receieved a scholarship to study there. Though it is likely (though by no means certain) that I would hear back within the next week. Hence why I was considering requesting an extension from university B. Although university B is very good at this specialty, so I suppose they may have many students applying.

In many ways this PhD at B would be convenient in terms of proximity to home and other research institutions which have people I want to collaborate with. And also it is great that I could work on two areas. On the other hand:


I am not sure whether doing the masters at university A may lead to a PhD there, which would really really boost my prospects for good postgraduate positions.
I am concerned about lack of background. Ultimately, I want to do as good research in math as possible, but I have only had a year of learning pure mathemtics. I have no problem self-studying, but it would chip away time at my PhD when I would expect to be doing paper-worthy research.
I keep getting this nagging feeling that maybe I could have better PhD positions; from universities that are more widely reputed in math in general. Though I oscillate between feeling like this, and thinking that I should be grateful that anyone thinks me capable of doing good math research having only a year of math behind me.


I am meant to respond to university B by tomorrow. I'm not sure whether I should read into their relativity short decision period or no- perhaps it is like this because they really want me, or perhaps because they have many good candidates applying to whom they could be offering the funding. In general though, I am incredibly stressed by this. I genuinely have no idea what to do. I also an somewhat biased by the fear of getting old in postponing my PhD another year.
You're stuck in a conundrum you'll encounter all through your life: You have a girl/boy friend and you wonder whether it's worth committing and getting married -- but you keep wondering whether anyone better might come along eventually. You have a job offer from a well-paying company, but you still have that application pending with Google. You have a grad school offer from University B but you're still hoping for one from University A.

The point is that sometimes you just have to commit. Your tentative second choice isn't going to wait for you forever while you're trying to figure out whether sometime (or someone) better might come through: Universities, employers, and partners make offers that are only valid for a certain amount of time because they, too, eventually want clarity and the ability to plan going forward. That's just a fact of life.

In your current position, you can of course ask for an extension, but you should be prepared to not get one. You'll then (i) have to make a decision that takes into account how much worse you think option B is compared to option A, and how likely it is that option A comes through, and (ii) find a way to make your peace with your decision. In fact, finding ways to be at peace with your decisions is what I think is the key piece to a happy life in general.