How PhD projects are acquired in pure mathematics In pure mathematics (please only answer for this field, as other areas are different), what is the ratio of PhD students finding a project on their own, versus working closely with their supervisor to find a project versus the supervisor giving their student a project?
As mentioned by Buffy in the comments, you're unlikely to find an actual ratio to answer your question without gathering some data. However, it seems like your question is actually where your research project would come from as a PhD student in pure math.
The answer is quite simple: it depends on you and your advisor.

Have an idea for your project? Tell your advisor about it and get their feedback! A thesis project (or even a side project) needs to be both interesting and manageable within a restricted time frame. One of the main reasons you have an advisor is to learn how to ask interesting but manageable research questions. Your advisor's experience is a valuable resource for learning this skill.

Want your advisor to give you a project? Ask them about it! Some advisors have lots of project ideas and are happy to share them with their students. Other advisors will be more hesitant to give you a project -- I know some who think it is important for students to come up with their own questions.

Want to come up with your own project but don't know how? Tell your advisor and ask for advice! They will probably tell you to read lots of papers, listen to lots of talks, and ask lots of questions. You can tell them the ideas and questions you have, and then you can ask if any of the questions are interesting. Again, asking research questions is a skill that you need to develop.


A corollary of this discussion: don't just pick an advisor based on their research area or whether or not they're &quot;famous.&quot; Every advisor has a different approach to research and mentoring, and you want to make sure that your advisor's style is compatible with your personal working style. If you don't like the idea of your advisor making you find your own question, or if you have your own idea for a research project that you want to pursue, then you should be sure to ask potential advisors about this before deciding to work with them.