Ok,I don't have much time to chime in here,but I'm so moved by Tom's post,I feel compelled to.
Tom,my career has been a long road of disappointment and agony. My prime years were spent caring for cancer stricken family-particularly a father who died slowly of prostate cancer for 18 years before mercifully passing 2 years ago. To make a very long story short,it dragged me from a double honors standing in mathematics and biochemistry to an aged, sickly graduate student in pure mathematics barely squeaking by.My career suffered a major last setback when I was forced to take courses for a year and a half to maintain my health insurance,which lead to subpar performances that dragged my GPA down to barely 3.3 from a nearly 4.0. I now need to take my oral exams,get my masters' degree and try and work for a year to support my elderly mother and myself for a year before entering whatever PHD program will take me.
My point is I haven't given up either and you're absolutely right that in published research lies your salvation. I think Erik's given you the best career advice of all the responses so far. The right connections combined with both strengthening your background and diving into journal reading and writing can turn your fortunes around quickly for the best.
But it's absolutely critical you don't founder for 2-3 years doing this.
My advice?
1) Write up a career plan on a calendar with dates and set goals for yourself. Don't set unrealistic ones.For example,don't print out a list of the Millenium Problems,pick one and say that's your ticket to Harvard. (Well,anything's possible,but don't set that as a goal!)
2)Comb the internet for unsolved problems and try and find some that look like they can be attacked reasonably quickly and with some success. Combinatorics and number theory are loaded with these. Start reading significant papers that aren't over your head,get yourself a black notebook and start scribbling. And make sure the notebook never gathers dust no matter how little you write in it per day!
3) Find prestigous professors you either know or think are approachable and try and make connections with them. For example,I'm a religious attender of Melvyn Nathanson's number theory seminar this summer after attending a research level additive number theory course with Dr.Nathanson last year. He's a warm and brilliant man and so far,that seems to be working well for me. I hope to get him to agree to do research with me after delivering a few talks this summer and fall at the seminar. Most exciting-I'm going to try and take Dennis Sullivan's advanced topology seminar this fall and hope that leads somewhere.
You are definitely not doomed. But your GPA is a black stain on your academic soul,don't kid yourself. You now need to show people it doesn't accurately reflect your talent. This will be a much harder road to travel then a 16 year old prodigy taking honors analysis at Harvard his freshman year,no question. But this is not a road to nowhere unless you let it be.You just need to make smart choices from here on out and don't give up.
Good luck!
