Some background: I'm currently about to finish my first PhD year (in a 4 year program) in complex geometry and I'm really struggling with it because I have to learn a lot of new mathematics essential for the area and which are completely new to me. My background is not completely in mathematics. I did my bachelor in physics and computer science, and after that I obtained a masters in pure math, where I got to learn the foundational material (analysis, topology, number theory, etc.)
As a consequence I've contemplated the following options:
The first gambit: Continue with it and give it my best try. I'm confident I can learn all the material I'm required to, the problem is my learning speed is not fast enough.
The second gambit: Change to a more friendly area: I'd like to think of this as an area that requires less foundational material (more vertical perhaps?). An area which may be better suited for me according to my background AND for which my university has a group for it (this limits the options). One of the options would be applied math.
The solution I fear most: Quit the PhD. I really don't have the slightest idea what would be of me in this case since I despise the idea of working in a 9-5 job, it's just not my thing.
In fact, all this got triggered by my advisor showing concern about my progress a few months ago, and as of now, they told me to learn certain topics, yet I find them quite hermetic given my foundational gaps, so I often get very stressed while studying this foundational material since I should be also studying what I was told to.
At the moment I'm not personally ready to take options 2 or 3, but these ideas are always in my mind.
What this post is for: I'd like to know what other people in similar situations to mine have done and how it worked for them. Maybe I'm overlooking other better courses of action. Maybe it's normal to feel this way or have some of this problems, or not. Broadly speaking I'm looking for advice from a more experienced person.