Is it a good idea to take a break from studying a mathematics PhD and revisit academia at a later stage? In September I started a mathematics PhD at a UK university straight after my undergraduate MMath degree at a different university. On the whole, I am enjoying the experience. However, I've been having recurring thoughts that perhaps I am not cut out for doctorate level work and it might be a good idea to revisit mathematical studies at a later stage. 

Basically, since coming here I've been feeling consistently like my heart isn't in it (and this has had a negative effect on my work ethic). This is not necessarily because I’m not capable of doing it, but rather because I never had a proper break from academia and I feel like I've been running out of steam. I know PhD students very frequently go through spells of feeling dispirited, but I feel that if my heart is really in mathematics that this shouldn't be happening. I would rather go into doctoral studies with a running start knowing that I am adequately trained in the area I am in, rather than adjusting to a learning curve (and an inexperienced supervisor). 

Here are some options I have considered:


Having a complete break from academia (6 months to a year), followed by a period where I slowly ease myself back in at my own pace by reading.
Taking CDT (Centre for Doctoral Training) courses. I had previously applied to this and been rejected, but now I think I would be more competitive. I think this rigorous training would be helpful for me. 
Doing something altogether different -- learning another programming language and doing a programming job, or working in simulation/modeling at the Met Office, or another company that relies heavily on fluid dynamics. Or maybe even the EPSRC (which is where a lot of the funding for PhD mathematics students comes from)
Getting a normal job to demonstrate people skills, and saving up money to do another Masters programme, which will put me in a very good position for my PhD.


After doing the above, I could return to a PhD programme much
   later, when I am a much more mature person with a
   better mindset towards my work.

Thankfully, my parents are willing to support me emotionally and financially while I pursue any of these.

My question is whether this is a good plan. In particular:


Is it a good idea to take a break from studies if wanting to
continue them at a later date, especially for mathematics? Would it
hurt any opportunities later on down the line to take up a PhD a
year or so from now?
Would my department or supervisor think badly of me for wanting to
terminate my studies - and (generally speaking) would I not have to
pay back the studentship instalments that I've been paid so far?
(I've been funded solely by the University, not by a funding body
such as the EPSRC).
What would be some worthwhile things to consider doing during a
break from academia?




Update: it sounds like this would not be a great idea, and I should only make the move if I am really, really convinced about it. Nonetheless, I'm leaning further and further towards it because I think it's better to take a break from my studies now rather than 3 years down the line. I don't seem to have the motivation required to be a good doctoral student at the moment. This is something I might speak to my advisor about.
Is it a good idea to take a break from studies if wanting to continue them at a later date, especially for mathematics? 
  


That's a tricky question.  There are probably some people for whom this is a good idea, but I wouldn't say it's generally one.  If it's possible in your current situation to essentially hit the "pause button" on your studies and be guaranteed the ability to come back (I think this is possible at many US universities), it might not be so bad, but otherwise you're taking a pretty big risk.  Also, in even as short a time as 6 months or a year, you risk forgetting a lot.  Certainly this is something a lot of other people I know who've taken breaks (say between undergraduate and graduate degrees) have mentioned. 

I would think about trying to arrange a shorter vacation (maybe 1 month) first, and see how that feels.  Taking a whole year is a genie that will be hard to get back in the bottle, and you don't know how you will feel, say, two months in.


  Would it hurt any opportunities later on down the line to take up a PhD a year or so from now?


It certainly might.


  Would my department or supervisor think badly of me for wanting to terminate my studies - and (generally speaking) would I not have to pay back the studentship instalments that I've been paid so far? (I've been funded solely by the University, not by a funding body such as the EPSRC).


I can't speak to them (or speak about the financial aspects), but probably it will not look great.  You should be prepared for everyone in the department to assume this means you are dropping out, no matter what you say about coming back.


  What would be some worthwhile things to consider doing during a break from academia?
  Has anyone else on here had experiences of a PhD (particularly maths) not going too well and feeling like they have had to stop or recharge their batteries?


I do know of one situation where this worked out a very well.  A friend of mine in grad school took a year off (after 3 years in the program) to teach in an inner city school.  I think at the time he started he was not so sure he wanted to finish, but the experience motivated him very effectively to go back and complete his degree, since he realized teaching middle school was definitely not for him.