i think that, once again, that i spoke too soon. in regards to an earlier post while i was on holiday, the technical details don't work out after all. so .. no theorem: not yet.
maybe i was spending too much time in the sun, not thinking clearly enough.
more likely i think that i've been focusing too hard on this one conjecture. odd: a year ago, i wouldn't have cared about it or thought much about it. besides worrying about finishing a thesis, at the time i was obsessed about, er ..
.. a different conjecture. [2]
at any rate, maybe i should let it go. at this point i care too much about it, and that affects my objectivity and creativity. i should be working on other things and learning new things.
even if i did prove this thing, so what? in maths just as in sports, it's important to know both the score and the game clock.
i think i've reached a peak in my productivity, in this research area. i don't think i'll get any more good ideas (assuming the ideas that worked are really that good).
soon i'll have worked on all the things that i want to work on. soon i'll have to move on and find something else of interest, something i like enough so that i can work and prove new things and write papers ..
.. because at this point in my career, i really need some more papers.
[2] as for why i switched from one conjecture to another: i think i have a proof for the earlier conjecture.
however, the argument i have in mind is long, technical, and not as interesting as i would like it to be. at some point i'll sit down, write it well, and see if i find any subtle flaws.
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