Writing About My Research

I never know what to say here about my research. Probably a significant number of people reading this wouldn't understand it at all. (Concisely stated, I'm looking at problems that are related to an extention of Grothendieck's generic freeness lemma to a noncommutative setting and trying to prove/disprove whether certain consequences of that result can be extended to more general classes of algebras. In a sense, it's a question of which algebras have enough "nice" properties for meaningful results to hold.)

The process itself isn't that blogworthy, either. Unlike the people who can blog about the creation of an outline or the number of pages written, or whatever, there's nothing tangible to show for my time. I sit for a while, staring at a blank piece of paper. Then I might re-write the question on the paper. Maybe I'll write some follow-up questions. Stare at the paper some more. Flip through a related article, hoping that something will pop out as useful. Sometimes I'll take a section of the article that I'm reading and recopy it (like a medieval monk) onto my sheet of paper, just to be sure that I'm understanding every line. Maybe then I'll instead stare at the wall for a while.

It's only after a while of this (for me, this takes months and months) that a good idea might pop out. Then there's the business of nailing down all the details and making sure that the idea really does work -- that it's not some sort of trick being offered by my brain to get me to stop staring at empty pages and walls and whatnot. (Ideas that arrive in the middle of the night are almost always wrong.) Only once an idea survives this personal vetting process can writing begin.