A few years back, I did an undergrad double major in math and physics, and afterwards went to a top-tier university to work on a physics Ph.D. Around about my third year of the Ph.D., I started to feel like my research was not really going anywhere, and I had serious thoughts of dropping out. I sought out advice though, and the word I got was always "Everybody feels that way in their third year. Stick it out and it will get better."
Unfortunately, it did not get better. I'm now in my sixth year of the Ph.D., and in all the time I've been here, my entire research group has only published one paper. It may take another year or two before I get to be lead author on a paper, and even then, I don't think the paper will be very good. Moreover, I have little desire to do this work for the rest of my life. And so I am again thinking seriously about what alternative options I have.
While I've published no physics papers in my time at grad school, I did publish two small notes of original research in Amer. Math. Monthly on my own, and even though they're not terribly consequential papers, I'm happier about them than about my "official" research. I enjoy math research, but I don't think I know enough to do it professionally (my physics research is not something like gauge theory that is of direct interest to mathematicians). I've been considering dropping my current program and starting over in a math Ph.D. program, but it's not clear to me whether this is a viable option.
So my questions are whether good math Ph.D. programs would be willing to take a person like myself? How damaging to my credibility as a researcher would it be to drop out of a Ph.D. program? Should I even mention that I was once a physics Ph.D. student, or just leave a big blank spot in my resume for those years? And finally, if this course of action is realistic, how should I go about getting recommendations (I would not expect my advisor to be very happy if I dropped out, and I have no real connections in the math community at this point)?
Obviously, I'm not going to do this without careful consideration of many factors, but I wanted to solicit the view of people in math academia on whether I'm being at all reasonable, or if I'm just a crank.
(I can provide some more situational details if it is necessary, but I would like to maintain anonymity and genericity to the extent possible.)