There are two sides to this; I believe that indeed you should have more supervision than you have, and that your supervisor doesn't give you remotely as much help as you deserve and should have a right to receive. On the other hand you may be right about not yet being independent enough and that there's some skill set that you need to learn.
There is a huge variety of supervision styles and supervisor behaviour and your supervisor is certainly far on the "hands off and rely on student's independence" side of things. There are supervisors who support their students much more, however your supervisor is by far not alone with his interpretation of his role. Unfortunately, for many PhD students this will not work (you are absolutely not alone with this problem).
"According to him, doing a PhD is about becoming an independent researcher" - that's fair enough, but surely it's not about being an independent researcher already, which he apparently expects you to be! A good responsible PhD supervisor should lead their students into such a position rather than assuming that the students get there on their own!
Not sure to what extent you already tried to get more help out of your supervisor. Surely "independence" also means that if your supervisor tells you "leave me alone and find your own problem" you shouldn't necessarily just say "Yes, supervisor!" Being "independent" as a researcher doesn't mean not to talk to anyone, not to admit where you are struggling, and not to ask anyone for help!
Maybe you can "milk" your supervisor better by telling him that and in what way you are struggling, and to ask him to talk more with you about the research he is doing and how a problem could be found for you that he is actually interested in and that may help his work somehow. Try to get out of him as much as you can, and if that means not accepting his initial idea about supervision, so be it. Also try to connect things that you already know to what he says. What do you like in mathematics, in algebra or elsewhere? What kind of problem do you like to work on (for a moment ignoring whether that would fulfill requirements for a PhD)? Can you somehow make a connection between this and what your supervisor is interested in? (You can also ask him whether he sees a connection.) There are by the way textbooks that have exercises that in fact are research problems in disguise, so looking at textbook exercises in the area might help.
Once you have a problem, obviously the first step is to look for literature and to find out how other people solved similar problems, and whatever you can find is connected.
In case you don't manage to get more out of your supervisor, I agree with another posting that you should contact somebody else in the department. Isn't there a person such as a PhD tutor to which PhD students can go with issues? Somebody more senior you trust? Student representatives? Ultimately the department should make sure you get enough supervision, and there should also be some point to go to for students who have problems.
The side of your own attitude is somewhat difficult to assess. Let's say I'm somewhat surprised that it only dawns on you 1+ year into your PhD programme that you have no idea what to work on. Would it be like this even in algebra or the area of math you are most familiar with/like most? Have you done a Masters project or something like that? How was it? Have you ever worked on a problem, even a set exercise or something, that made you wonder about whether something more can be done there than you were asked for, or where you even had an idea what else to ask or what else to do connected to the problem? You surely need some proper curiosity and drive for doing a math PhD. The problem of matching your interests with the supervisor better can in all likelihood be solved, as can the problem of generating suitable problems "between" your interest and the supervisor's. If your supervisor is not the best person for helping you in that respect, talk to others. However, if you don't have a genuine interest for research and some curiosity and drive, your position isn't that good.
I think in your position, without supervisor help, I'd have grabbed a sufficiently sophisticated textbook about something somewhat related to computational geometry and something that seems interesting to me, and would've started to work through the book, trying to understand more or less everything, do some exercises, with particular awareness for any hint what could be a direction for my own research.
Last remark about "waste of time" - it's an experience, and many PhD stories involve being stuck and feeling that it's not going forward for quite some time. If you manage to dig yourself out of such a hole, you will feel the success and with hindsight will probably think that this phase was a valuable part of the experience. Don't forget that as long as you're studying just the stuff others tell you about and solve the exercises they have solved already, you may learn, but you don't push science forward. If after three years you have spent half the time in a hole trying to find your way out, and half the time doing something that is really your own project, this is quite a bit more productive than learning stuff that was spoonfed to you and passing exams on it, be it with flying colours. Many PhD projects, particularly in math, don't lead to published papers in the first two years. When I got my PhD after 3 1/2 years or so, I only had a paper on some earlier work from my Masters project; it took almost a year more to get something from my PhD out - this was the old days when there was less pressure to publish though, but really still it can pay out to take time to try to get into things in some depth rather than going for anything that could be publishable on the quick.
