how fickle: fate.

that one particular conjecture remains standing. i cannot prove it in full generality and it bothers me. let me not say more about it, otherwise i run the risk of sounding like the type of mathematician who calls everything "obvious" or "trivial."

gee, buddy. i guess it's only deep, earth-shattering thoughts for you.
it must be really annoying, spending all day working on math and getting "nowhere."

yes: better that i shut up now.

---

i spoke with the supervisor [1] yesterday, and nothing came to mind.

then, last night, i had an idea. it pushes the argument further, but not quite a proof.

this morning was a confusion. i was stuck and couldn't "prove my way out" of one particular obstacle. i still don't know how to do it.

this afternoon, while recalling what i knew about the problem, i worked out a counter-example to a lemma i wanted. it isn't true.

dejected, i went to the gym and feeling miserable anyway, i decided to run on the oval track above the basketball courts [2].

around lap 10, i realised that the counter-example was valid only for the would-be lemma and NOT the theorem i have in mind. i then cursed my luck, because there were 14-15 laps [3] to go until i could willingly let myself leave.

around lap 15, i remembered a theorem which states that my counter-example is "not generic." yes, i'm not being very precise, but if you really want to know, it's Theorem 10.11 in Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability by P. Mattila.


so: i still can't prove the conjecture, my counter-example didn't work out, but now i know of one more thing NOT to try.

maybe i should stick to writing my thesis!



[1] to honor someone's wishes, i'm reserving the keyword "advisor" for my late advisor. paperwork keeps things running, but morally, i remain his student.

[2} i HATE that track. the conversion is 8 laps = 1 mi, so it takes a seeming eternity to gain any reasonable mileage. there are 3 lanes, and almost surely there will be 2-3 people running shoulder-to-shoulder, shooting the breeze and/or listening to their iPod ..

.. which means that to pass them, you need to switch a few lanes. it's extremely irksome.

[3] i can never keep count of laps very well, especially when swimming. sometimes i run an extra lap or two, just in case i miscounted.