For the past year, I have been trying to prove a theorem. This is what mathematicians (and aspiring mathematicians like myself) do: they sit around, testing ideas on pieces of paper or on computers, talking to colleagues, reading the literature, all in order to prove theorems. Theorems are the goals, the standards, the mileposts. She who dies having proved the most theorems wins, or at the very least, gets tenure.
For the past year, I have been trying to prove a theorem. A nice theorem, a pretty theorem. It basically says that there is only one way (up to a product) to specify a disconnected fractal. If this theorem were true, lots of other pretty theorems would follow, and several proofs of other theorems would become much simpler.
For the past year, I have been trying to prove this theorem. Technically, I should have called this theorem a conjecture, as it had no proof. But I believed in this theorem; I knew it was true, and that it was only a matter of time before I proved it. I had, at any given time, several possible proofs. Some were elegant, some were not. Some had big holes, some had small holes. Sometimes I wasn't sure if a proof had holes in it or not.
For the past year, I have been trying to prove a theorem. It has been almost exactly a year, in fact. I started working on it last August when I finished up my paper on fractal polytopes. I have been doing other things during the last year as well, of course: classes, homework, and some other minor research problems. But for the last year, whenever a lecture got boring halfway through or whenever I was caught on the T without a book, I would take out a piece of paper and work on my theorem.
For the past year, I have been trying to prove a theorem. Two nights ago, I discovered a counterexample.