I apologize if this is too long a post, but I could really do with a few pointers about my current situation.
I am 25 years old and I will complete 4 years of my PhD in a computational applied mathematics program in the US in August 2013.
My bachelors was in pure mathematics. I had gotten interested in numerical analysis in that time and so I had applied to my current PhD program. I have been under my adviser for 3 years now (the first year at my university is spent in coursework). A PhD at my university is usually 5 years long.
Right now, I have almost nothing to report in the way of research, and consequently no publications , no conference submissions. I am getting increasingly nervous and frustrated about whether or not I will make it, even if I give myself an extra year by funding myself.
My adviser has consistently been making me work on uninteresting stuff, where most of the work involved is purely technical like writing brain-dead code, with almost zero chance for innovation.
BREAKDOWN OF MY PHD
After monkeying around reading research papers, in the first year under my adviser, he got very confident about getting an industrial project and got me working on that, in anticipation that the contract would go through. At the end of the year we found out that we did not get the project.
In the second year, he said he wanted to get into GPU parallel computing and to implement a few fluid dynamics algorithms. I slogged over many manuals, spent months and months writing and debugging code, all the time thinking that this would be used to do some simulations he was interested in and get them published. But at the end of the second year my professor completely lost interest in these numerical techniques he was making my implement.
Seeing his capricious attitude, I almost wanted to quit then and there itself. But I decided to just stick it out, thinking it might be 'just a phase'. Due to funding issues, he once more got me working in the third year on another project which essentially involved writing a lot of stupid code, and running endless benchmark tests.
I have basically ended up trying to do a PhD in mathematics without any mathematics in this PhD.
Finally, a couple of weeks back, I told him that I had had enough, and to give me some actual problems/material to work with. After about an hour of discussion, and informing him that I was ready to fund my self if required, he finally gave me a couple of possible starting points for what I hope would actually turn out to be worthwhile research.
I do realize it was extremely foolish waiting for so long before putting my foot down, and not having the courage to speak up before. My adviser is well-regarded by colleagues in his field, and maybe I was subconsciously scared of contradicting his handling of my PhD for pissing him off.
But even though he has now suggested problems which do seem interesting, after having had so many negative experiences I am very skeptical about the future. How should I proceed, and what are the factors I should consider ?
Frankly, I am feeling very burned out. In the way of future plans, I have been toying with the idea of dropping out, getting a break for a few months and then sitting for some entrance exams for a Masters in Economics in some good universities back in my home country. I always found economics very interesting through my undergrad and more so these past few-months while studying it has a hobby.
Continuing would require me to stay on for an extra year till August 2015, which leaves me about 17 months tops from now, before I start hunting in academic job market. This includes about 2-3 months I will have to spend doing literature review on the proposed topics and learning the requisite mathematical tools.
So if I decide to stay on, how should I re-structure my study/research time and the relationship with my adviser in these 17 months so that I can make some head-way.
Maybe 17 months is too short a time? Any suggestions would be really helpful !!