Ph.D. work seems like a drag sometimes, is this normal?

This is quite normal - it is possible to be passionate about the topic, but at times, to be not so enthusiastic about the work involved. This could be a sign that you are need of a bit of a break, or in the worse case, heading towards a burnout.

A few things to reflect on:

• Are you getting enough sleep, exercise and eating well?
• Are you making time to visit and go out with family, friends and other like-minded academics?
• Are you giving yourself some time out to pursue other interests and hobbies? There would have been times that the greats of the topic felt the same.

These greats of the field more than likely had days when they also could not be bothered.

Specifically, why not consider the following:

• The days when the mathematics is very difficult, take these as challenges (rather than hurdles) to accomplish (rather than just overcome)
• Teaching the class could be opportunities to refine your mathematical (and mathematical communication) skills and similar type of skills.
• Is there anything you can change to make your situation more enjoyable?

It is very normal.

I think it's perfectly normal. While I am myself still learning to be a PhD student in a fairly math-intensive area of research, I want to share my thoughts, expressed beautifully in this comic: If you try to chase 'fun' each day as a PhD student, that might be being a bit unrealistic. Instead, try to find 'fulfilment' in your work.

Set aside a medium-sized, actionable goal for two weeks, for example: "try three completely different approaches to prove this lemma that I need". Or "write up the detailed analysis of this algorithm". That two week deadline you set for yourself to finish something which you know you'll be proud of will up your motivation (at least for those two weeks).

I have another strategy for motivation-less days when I don't feel like doing research, don't feel like reading papers, don't feel like preparing to teach, but actually need to make some progress academically: I have a lot of researchers I admire - my own advisor, the giants in my field, the rising stars winning all the recent best paper awards, etc. I have many of these people's theses downloaded onto my laptop. On days that I feel zero motivation, I actually open up a thesis and start reading it. As I finish a chapter, I am overcome by the feeling of awe that what I read was a product of intense hard work and days and days of failures followed by that one success. It makes me want to be like them and therefore go right back to work (and I also end up learning something new).

And of course, on some days, you could just do something non-academic that would make you feel good about yourself - go for a long swim/run, finish a jigsaw puzzle, cook something complicated, etc.

Don't worry! Good luck :)