Changing PhD supervisor 18 months into 4 year PhD I am currently 18 months into a 4 year PhD in Algebraic Number Theory in the UK and I am not at all enjoying the work (I haven't been for about 6 months now). This is not because I am "stuck" - I am not really at a point where I have been able to engage enough with the work to even become stuck. The problem is more motivational: it turns out that I just don't have any interest in my particular area and so I spend most of my time either worrying about working or worrying whilst working - very inefficient! The area in which I work is also quite small in the sense that very few (in fact, only one that is comprehensive - as far as I am aware) textbooks have been written on the basics and even my supervisor admits that these few books are exceedingly dry. 
With all this in mind, I decided recently that I will leave the PhD and do something else (I actually have no idea what yet). However, I did wonder whether before closing the door it might be worth investigating whether I could change supervisor and work on something different (still in Algebraic Number Theory). I guess my question is whether others on this site (PhD students or PhD supervisors) have had a similar experience or have any advice regarding this situation?
Note. I have no doubt that this post will almost instantly be marked as "off-topic" - however I really think that it is difficult to obtain the opinions of professional mathematicians on other forums whereas (quite often) they respond to questions of this type on this site.
Many thanks!
 A: I think I can offer some wisdom on this. 
I struggled in the first year of a PhD in computer science but I succeeded at the end and gained a scholarship. My second year, however, didn't improve despite making another breakthrough. At the end of that year the powers that be in my department agreed to giving me some time off in order to put my finances in order.
Subsequent to this they have also agreed, at least in principle, to let me take my PhD to the mathematics department, and possibly my scholarship with it. The reason for the move is that I have become increasingly interested in the formal verification of mathematics and have devoted all of my spare time to writing a proof assistant. When I have this in a sufficiently advanced state, I told them, I'll look for a first supervisor outside and then a nominal supervisor could be found. This was all somewhat hypothetical but there was a problem with this plan anyway: software takes a long time to write! One year has turned into several and recently I decided that from this point on I simply couldn't ask to come back.
I now for the wisdom: it really doesn't matter.
If I recall, Timothy Gowers wrote a year or so ago that mathematics is a calling. Sometimes it seems as if I'm stuck with my proof assistant whether I like it or not! Thoughts of an academic career are completely beside the point. I honestly can't see what being inside of academia would give me right now. Less of an income, probably. (joke)
So if you are cut out for some sort of mathematics, I reckon it will come to you in time. You may not be able to help yourself. But don't think that such a calling is necessarily tied to a career in academia, because I think that this is increasingly not the case, and probably never really was.
