No, I can't. Not for a while. Because I can't seem to figure out the things I'm supposed to be looking at, and because I distract myself by other things. One of the other distractions, recently, has been playing around with polynomials. If you've been following me here recently, you've seen this already. What you haven't seen is what's happened since then.
I decided to try out WordPress, because I knew it had good built-in support for LaTeX, which Blogger doesn't have. So, over at sumidiot.wordpress.com, I've been keeping a more regular log of the work I've been doing, which in the past few days has only been messing about with quartic and quadratic polynomials. And I think I'm about done with them. I have determined when a quartic can be decomposed, and what it's decompositions are. The final result seems to be that it is the composition of two quadratics iff it is symmetric around a vertical line. I won't redo all the equations and things, because they're already at the above pages.
So... I know that's not thesis quality work. It's probably something people have done before, and it took well under a week to work out. All the same, it's been the most independently motivated I've been by working on a math question since playing with FLT in high school (yes, I really did - and no (clearly) I didn't get anywhere). I've had a great time playing with this question, and I've still got more I'd like to look at. In the mean time, I really ought to be thinking about my actual research, which is, sadly, entirely unrelated.
I've also been trying to decide what to do with that wordpress account. The subtitle I've currently got up there indicates it might be a fork of this blog, for the mathematical content. I've debated about trying to use it regularly to just write up whatever I've been looking at - for research or for fun. Writing things up is good practice, and helps organize your thoughts. Both of these would probably be good for me. Do I drop this blogspot page? Or drop the wordpress one? Post weekly wrapup links from here to the wordpress page? Post wrapup links when some sort of progress has been made? I guess time will tell. I know you all can't wait to see what happens. I'll keep you posted. If Blogger would just natively support LaTeX...