Doing math

From the blog of a mathematician I read (I don't know the mathematician personally), describing the way she does research:

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.


That's pretty much dead-on to the way I work, too, although a lot of the time I'll be laying on my back on a couch or my bed with my eyes shut, only apparently napping, or in a coffee shop sitting there, staring blankly and muttering to myself. Working on a philosophy problem really isn't all that much different for me, although I prefer to make philosophy-related notes on a yellow legal pad, and math notes on featureless printer paper.

Watching academics work must be as exciting as watching paint dry.