I got my Master's degree in mathematics in 2017. Since then, I haven't done a lot of maths, so I am a bit rusty. I am now considering doing a PhD in maths, but I have little-to-no idea for a topic.
I seem to understand that it is not unusual for prospect PhD students to be without a topic at first and be sort of "assigned" one by their supervisor, but I think I would nonetheless benefit from having at least some sort of idea. Ever since I picked up math, I think I've been more drawn to more abstract and theoretical math and not at all to applied math. I am fascinated by number theory problems, and I like algebra so I thought I could do something related to them. My bachelor's thesis was on algebraic topology and my master's thesis about wreath products and the Rubik's cube. However, PhD my topic doesn't necessarily have to be related to these. I can't say I have any preference at this stage, and I'm trying to find one.
I tried to get some inspiration by going to the campus library and checking out different books, but that didn't work well for me. Most books are extremely technical and you can't just flick through one to get a sense of whether you like the subject or not. (More often than not, the title won't even tell you if the book is worth picking up.) I tried googling, reading Wikipedia, etc, but I can't say that helped, either.
What I'm after is some sort of overview that presents problems in different fields, explaining why they're important/intriguing, where we're stuck with them, pointing out connections with other problems or branches of maths. Something that tries to "sell" you a topic, if you will.
I'm not sure such a thing even exists, so any suggestion you might have to help me get an idea will be much appreciated.