interlude: a list of challenge problems.

yes, i did promise that i'd talk more about how math is going for me lately .. but i didn't say right away. q:

in the meantime, i stumbled upon this post from ars mathematica about 23 problems that D@RP@ (Defense @dvanced Research Projects @gency) has challenged the world to solve.

[PDF link]

they're rather applied sorts of problems and a few which are biological in nature, but one includes the Riemann hypothesis.

in transit.

back in ann arbor .. essentially, anyway.

i started typing this post on a michigan flyer bus, which is a shuttle from detroit-metro airport to ann arbor, detroit, and perhaps east lansing: i can't remember. after reading that it went from AA to DTW, my interest vanished like a smooth test function outside its support.

at any rate, it offers free wireless internet and if i heard correctly, free bottles of water (i haven't checked the cooler up front, yet). rather pleasant, actually.

as for any math done .. not much: more to come, about that.

mathematics, jobs, research meetings, and holidays.

in retrospect, perhaps i should have attended the AMS joint meetings this year, after all. (so L, if you're reading this: yes, you were right.)

a few schools (those with tenure-track openings) have written me to ask if i will go, which i will not. the question is:

are meetings and interviews there really not mandatory?

and then, the deeper question follows, which i have been consistently avoiding:

where do i want to go?

as for my usual response,

it's a dangerous thing to want something.

---

on the plus side, my third letter of recommendation appeared on mathjobs today. (:

but to add to the minus side, i haven't gotten back to thesis-writing yet, though i'm still on holiday and visiting family. i promised a postdoc friend i'd talk math with him on friday, so at least that should keep me honest; his questions will further keep me on my toes!

i did think about a little mathematics, today: one of my old lines of argument. i don't believe that it's wrong, but when does anyone truly believe that they are wrong?

time's up: now, the holidays.

something's not quite right with a recent proof i had in mind. there's a gap in the argument and i can't seem to patch it. i still believe that the result is true .. just not quite a proof yet.

tomorrow's a trip home to see my parents. i decided on three days off, which isn't much anyway because day one is for travelling. tomorrow is:

8:30am airport shuttle,
10:00am flight,
.. then noon,

and life begins again:
lunch and family,
but not mathematics.

day three is christmas tuesday. i'm not religious and my family's not religious.. but somehow it's christmas. you shouldn't do math on christmas, should you?

at least not on christmas morning?
even if you don't have any presents?

..at least, i don't think i'll have any presents..

mathematics and holidays.

it's hard to concentrate now. in retrospect it would have been better to have taken a holiday this week and then go back to work next week.

then again, that would have been uncharitable to my family. i'm visiting them next week and though we're not religious, it is christmas-time and we have our own little rituals.

here's the paradox:

in the week or two before visiting my parents, i never feel like doing any math ..unless it's going REALLY well, of course.. and when i'm there, well..

.. there's nothing to do.

we mope around at home, albeit in familial togetherness. it's too far and unsafe to walk anywhere, because highways partition that suburbia; we don't have cable or high-speed internet, either. with six people under one roof, it's hard to have any solitary time, to let one's thoughts wander.

it's almost a counter-reaction:

there's nothing else to do, so let's do math.

meanwhile, i'm blogging and twiddling my thumbs in procrastination.

i've already scanned through the "headlines" (i.e. title/abstract/author lines) of recent posts on the arXiv, as well as the maths preprint servers at jyväskylä, helsinki, pisa (SNS), leipzig (Max Planck), and prague (KMA Charles Uni). i've done my "window shopping" for conferences in 2008, despite the fact that i'll be too busy to attend any between now and may.

then again, just because you can't 'afford' certain things, it doesn't mean that you can't look longingly at the sale exhibits.

every so often i'm tempted by honesty and i peruse a rough first draft of section two of chapter one of what-will-be-the-thesis.

maybe i'll find the willpower later, later today. maybe it's not so bad, to take a break now, and get back to it. that's the beauty of academia, right: to set one's own hours, for best creativity and effort?

i keep telling that to myself, but remain unconvinced.

all a mystery..

i would say that geometric measure theory is one of my mathematical interests. it would be too late to say otherwise, anyway: i've already listed it as one of my 'research interests' on job applications.

i think i would like gmt much more,
if only i understood any of it.

mathematician's block: the curse of notation.

yesterday and today didn't feel much like work. i've been trying to understand a "proof" that i wrote two months ago.

the good news: it still looks like a proof. i haven't found any flaws or counterexamples yet.

the bad news: i can't seem to write it well.

you see, there's some funny induction in the argument. each time i write it down, the notation obscures everything. the frustrating part is that the case of dimensions 2, 3 ..even 4.. they work out by hand.

so it's possible that it will work out nicely. i just can't seem to find it out.

in memoriam.

as friday turned into saturday i began to think of this weekend as memorial weekend .. not memorial day in the calendar sense, but a memorial day for the advisor.

he died on october 30th. since then, every morning i've woken up, never sure if it would be a bad day. "bad" doesn't mean a bad math day; i don't bother worrying about such things. instead, "bad" means that the mathematics reminds me

• that he died, and that i will never see him again or share in his insights;
  
  
• that he would want me to carry on the work, improve intuitions into ideas and arrange ideas into proofs;
  
  
• that there are more qualified minds than mine. i cannot do justice to what could become an amazing problem or a beautiful theory, if only it were put into the right hands ..

.. but there is no one else. only i was there, in that very time and place, and if the advisor's ideas mean anything, then there is no real choice in the matter.

i have to see them through, but that only makes it harder.

---

i've written before about this weekend, and about the nature of funereal gatherings. one sees family and friends and for that, one is happy. on the other hand, none of us have any illusions about why we are there.

a few friends wrote me early, suggesting that we talk math in the time before the memorial service. the thought troubled me, at first, but then it occurred to me:

with such a critical mass of analysts and geometers, the advisor would have laughed at us if a few theorems didn't come out of that many days of conversation.

so we talked and laughed. we posed a few problems, and we might have proven a theorem: we'll know once one of us decides to write down the proof.

life goes on, i guess. this is not to say it's easy, but it goes on.

about jobs, and the law of conservation of anxiety.

it's slightly disturbing to apply for a job, then to see that the job opening has been re-posted.

it's my inferiority complex at work, of course: i become inclined to suspect that their applicants are not "prestigious enough"

      ..among them, me..

and that they want someone smarter, better looking (at least on paper), and more published.

---

i'm becoming less worried about applications, but the law of conservation of anxiety persists: i'm more worried about writing/finishing a thesis, and this makes up for it!

two anxieties.

1. in my (forthcoming) thesis, i will have a theorem which is relevant to measurable co-tangent bundles on a certain class [1] of metric measure spaces.
   
   one requires two other theorems for this application. i've been working on writing a good proof of the first theorem, which reduces to a lemma.
   
   so far, the proof of the lemma takes 2 pages (standard amsart format) and i think when it's done, it will be 3 or more pages. possibly 4.
   
   i have a bad feeling about this.
   
   
   
2. i am ambivalent about this weekend. on one hand, i will see many friends and familiar faces. on the other hand, the reason is a tragic one.

[1] too technical to say, here; those of you who know me well will probably know the exact hypotheses.