There have been previous questions related to mine; for instance, this one:
Losing faith in my PhD advisor?
I believe this new question is worth asking because of my specific proposal for action.
I am a PhD student in mathematics in the US in my final year. My advisor is not a competent mathematician, and does not really understand even the basics of the field he is supposedly working in. Please understand that I have come to this conclusion slowly and reluctantly; I am well aware that, for instance, people can say "dumb" things in the moment.
Anyway, I've been on my own as far as learning this field and producing some research. I feel like I've just gotten to the point where I know what I need to understand to work in this field, and if I had another year to actually learn it, I could start really doing research. Essentially, I feel like this is where I should have been a few months after working under my advisor, but it's been 2.5 years.
Unfortunately, I feel like it is probably too late to switch advisors or schools. Staying an extra year with this advisor may be an option, but would be difficult financially.
I think I will be able to produce a dissertation and graduate this year. My dissertation will not be a work I am proud of. My idea is that I could get a postdoc and make up for lost time there, really learning my field and establishing a decent research track record.
While this plan is very distasteful to me (of course I am not happy about producing work that embarrasses me), I want to ask about the practical aspects. What are the chances I could actually get a postdoc? My advisor seems to think this is very possible; but other people lead me to believe that as someone with no significant research results and no one with prestige to recommend me, it is unlikely. (I no longer trust my advisor's advice on anything.) Assuming I obtain a postdoc, is it likely I could establish a decent track record of research, given that I will be in some sense two years behind schedule as far as learning this field and establishing myself?