Advisor is providing little help, but also I'm not that good. Help?

[telemann314]

So I'm about to finish up my fourth year of a PhD program in mathematics.
I cruised through my comprehensive exams and coursework, and then hit a road block trying to find a good advisor. I did reading courses with all my top picks, and all of them were "full" and so couldn't advise me, or left the school, etc. So at the beginning of this year I ended up finally settling with this advisor who is like a top 3 researcher in his field, BUT a) he has like 10 students, and b) his area is basically the hardest thing ever, and his students routinely take up to 9 or 10 years to graduate.

I have been working with him for about 2 years, and I just don't feel like it is going anywhere. I don't have a research topic, and haven't done my prelim exam. Our meetings basically consist of me asking him questions and him answering.

Now, I absolutely love working with him, and we discuss so much interesting and cool stuff. But, I don't feel like he is helping me learn how to do research in math, or helping me find a research question. When I asked about this, he said he's just not that good at giving people questions to work on. He says that there is basically no way to do a PhD in his field without a lot of time, and that 3 more years of PhD is like, minimum for me to finish.

There are also some other issues, like that the thing I'm the most interested in is something he has limited knowledge about, and that the area he is pushing me towards just seems unapproachable to me. He has suggested I go to the other people in my department and ask about these other things, but I have gotten nowhere with the other professors as they were people who didn't want to be my advisors, and aren't that interested in talking to me just for fun with no reward in it for them.

I really cannot imagine me being able to pull of research, let alone good research in this field without some serious help. I haven't published anything in pure math, and have no clue how to go about finding a research question, or how to actually solve it. I understand that your advisor isn't supposed to just hand you a PhD on a silver platter, but should I be able to expect at least some more hands-on support with learning how to do research?

It could be that I am just not cut out to do math research, but nobody has told me that and my advisors have generally had good things to say about me. I do think I am below the average intelligence of people in my cohort, but I think I have done a lot of work on learning my area, and understand a lot of things better than lots of other people who have completed successful PhDs in math. It could also be that I could do it but it would take me like 10 years.

 

I'm 27, and I don't want to be one of those people who is like 33 having just finished their PhD and starting life. 30 is basically my cut-off age for getting a real job. So I want to know if anyone has advice for this situation. 1. Is my advisor or me at fault in the lack of progress, and if it's my advisor, is it worth switching advisors (and hence subject areas) 4 years into a PhD having done 2 years of work in this area? and 2. Is it worth finishing the PhD at all given that I think it might take me an unacceptably long time and there's a good probability I will never finish.

 

Thank you