read, gap, compute, patch.

maybe the old saying is true:
nobody knows your own work better than you. [1]

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3 days ago i found a gap in one of the proofs in my preprint. having sent it to friends, two weeks ago, nobody caught it either ..

.. and people wonder why i don't post to the arXiv. \:

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to patch up the proof, i need one geometric lemma. it is literally a lemma from euclιdean geomeτry. after trying off and on for a few days, off and on, i still can't find a clean, simple proof.

so i've done what any sufficiently desperate mathematician would do: i started some explicit computations in trigonometry ..

.. which, yes, is embarrassing.
[sighs]

ah, well. at least it's true. then again, this is going to be a pain to put in LaTeX.


[1] this was told to me during a job application seminar when i was a graduate student. the point, i think, is to write a research statement that is not a technical mess to read.