despite careful reading and the topic was part of my prelim, the trace operator from Sobolev functions on a (Lipschitz) domain Ω to Lp-functions on the boundary of Ω still seems a mysterious notion to me. perhaps i simply don't understand the use of capacity well enough ..
.. so much work ahead, tonight and tomorrow morn, and so little yet accomplished. it's frustrating.
speaking of frustrating, on the maths community @ livejournal i've read a few recent posts of users (and probably students) who speak of mathematics with good cheer and unbridled optimism, that they "can't imagine anything better than learning something new every day."
that's fine and dandy, but some of us have theorems to prove and theses to write.
from recent experience, it is very hard to accomplish something which is mathematically worthwhile, every day, and though it is dangerous to compare, i dare say that the difficulty can be compared to making good art, composing a charming song, or writing fine literature. let me set a foot on the sand without tracing a line: mathematics is a branch of philosophy.
it may be a science to the rest of you and that's fine; i'll not refute that. but to me, it is first and foremost a kind of philosophy, and possibly the best kind. in mathematics, up to the fallibility of human mind [1], there is conditional certainty, and that is a kind of progress, isn't it?
[1] at some point i should discuss something about the recent-turning-old events of formal proof, brought up by Devlin and by Hales. it will involve this viewpoint of philosophy.
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