one of those days....

it's been a bad math day... actually a bad couple of math days.

one could see movies like good will hunting or a beautiful mind or proof and get the picture that all brilliant mathematicians eventually go crazy in the process of things... but really, after a weekend like this one, it's completely evident to me how math really *can* drive someone mad.... and i'm not even one of the super brilliant type people.

to make things easier for me, here's your math definition of the post: bijection
technically a bijection is a map that's one-to-one and onto, but in less "math-y" terms it's a special kind of function from one set to another set used to show that they're the same size. (please don't be afraid just yet)
for example
say i have a bunch of people in a room and i have the numbers 1-10 written on notecards, and i start giving notecards to people.

if i don't give more than one notecard to the same person AND i give a notecard to everyone AND i use up all my notecards, then that says there are exactly 10 people in the room (because i paired them up with the notecards), so the "giving notecards to people" function is a bijection from the set of notecards to the set of people.

that wasn't too scary, right?

math people use bijections all the time to show two sets of complicated things are the same size. usually it's not notecards and people. in my case it's a special kind of permutation and a special kind of sequence.

ok, so i can now safely say "bijection" in the rest of this post.

timeline:
december: i came up with a bijection from thing A to thing B. i was super excited

january - february: i studied for my oral exam and thought nothing about research

march: i wrote up a nice 4 page paper explaining my bijection from december

april: in anticipation of the conference i plan to go to in june, i double checked several places to make sure i was the first person to come up with this bijection (i don't want to present someone else's old result at the conference in front of a lot of people who are older and smarter than me, right?). abstracts for talks are due tomorrow (may 1).

two weeks ago: i hear back from one mathematician that yes, he proved the same result 8 years ago in his thesis, but he did it analytically, NOT with a bijection. he also commented that thing C and thing A have the same size and to his knowledge there's no bijection between them.

one week ago: i go to the wisconsin conference armed with this knowledge and think hard and come up with an idea for a bijection from thing B to thing C (since i already have a bijection from thing A to thing B, putting these together would give me a bijection from thing A to thing C)

for the past 7 days: i work hard trying to figure out the kinks... when my bijection idea works for 2815 out of 2814 cases, i have a hunch that i'm on the right track and just have some small detail to figure out, but after several days of trying, no luck... i spent 8 hours on this yesterday and 6 hours on friday not to mention other days before that spent thinking about this.

today, 4pm: while doing one more literature search to be extra sure i've come up with something new, even if i don't find the bijection from B to C before the conference, i come across a paper from last year that has a bijection from A to C. it's much shorter than what i have from A to B even, so i'm crushed

today, 5-8pm: chatting with eric about it, he convinces me that unless they're identical i still have something useful to show, especially since my bijection actually gives a way to count the darn things, not just show that they're the same size. i counter that it's much clunkier than the other bijection i found and only goes half as far. i don't want to give a whole talk on one bijection if it's been partially done already.

today 8:30-9:45pm: frustrated with math, i beat my time for walk/jogging 5 miles from yesterday by 10 full minutes... at least being irritated is good for something.

today 9:45-10pm: i vent to leigh about the same irritations with proofs/what to actually submit to the conference tomorrow, etc. she disappears.

today 10pm-now: still trying to figure out my bijection from thing B to thing C, and things look moderately promising but i'm still not convinced how significant of a result it is anymore now that it's more or less been done bijectively before even if my bijection is a new one... leigh reappears around 10:30 with ice cream.

seriously, teaching is one thing. that's a performing art of sorts, and you can get good at it if you want even if you suck as a researcher, but math research is a creative art... but not even just creative and please the critics... creative and either it's true or it isn't, not just some people like it and some don't... true or false. it's really frustrating to put many many hours into the "creative" bit and have nothing to show for it, or to discover you've been out-creative-d by someone else. i did hear stories last weekend of grad students who always would prove things, then search the literature and find their results had been proven before, but in the 19th century, and they'd be really excited about when they made it to proving things that had already been done but in the 20th century. i guess i can be happy that the relevant related material to what i'm doing was just done in the last decade? it's just such a rollercoaster ride between irritated for working so long at no result, elation at thinking you have something to show for your time, and defeat at finding it already done. (and no, i'm not extreme in feeling like this... every math person i know does in spurts)

end of rant.

in moderately amusing news, mental floss (my favorite magazine ever) has a "mad scientist of the month" column every issue... this time around is erdos (most published mathematician ever, and quite a colorful character)... so mental floss gets major kudos from me.

in other amusing news, i saw someone with this shirt at the conference last weekend and i found it hilarious. i ordered myself one yesterday, and hope it comes in time to wear to either my students' review session or final this week. :P (because i'm ever so encouraging of a TA).

seriously, done ranting... it's not like any of you will make it past my attempt at explaining "bijection" in everyday words paragraphs and paragraphs ago anyhow.

night.