Posted by: holdenlee | June 2, 2010

Math snippets


It’s been about one year since I missed my goal on USAMO, had a “breakdown,” and wrote my Math Experiences essay (which I posted exactly 1 year ago). Though the response to my essay was overwhelmingly positive, a lot of it was written in the heat of the moment and my views have changed a lot since then. I read over the essay in February and made some comments on what I wrote. Below are just more ramblings about related stuff.

12-6-09

Yesterday was the Putnam. It felt different from USAMO. Even though I didn’t stress out about it, though, I couldn’t sleep the night before. Weird, my brain kept getting crowded with nonsensical things, like having to do something to fall asleep, which doesn’t make sense, because I just have to let go to fall asleep. It happened before other math competitions too. It’s like being too tired, so the brain doesn’t make sense anymore, but not able to sleep.

Anyway, I wasn’t stressing out over getting a certain number of problems on the Putnam like before. In the morning I actually didn’t want to take the Putnam. I didn’t care about it anymore, not like it used to be. So once I got into problem-solving mode, actually I kinda had fun on the test. Anyway A5 was a group theory problem. My goal for the test was to solve any group theory problem on the Putnam this year, because I was taking algebra this semester and had done a lot of supplementary work on it. So I grinded A5 for an hour and a half, even though scorewise it may have been better to spend more time on A3, which was a lot easier than I thought. When I don’t care about winning so much I get more time to explore. As long as I don’t care about my score much. Which I didn’t. I said, I’d be happy with a few points.

Break for lunch. Discussion. People asking each other, how many did you solve, etc.  This was the thing I raged about in my essay. Like, asking each other’s scores for comparison, to see whether one did better or worse. It’s weird, I avoided Olympiad/ competition stuff this summer but I seem to be getting drawn back into the spirit of things. I told others how I did, asked other people what they got. It’s friendly though.

[…]

Anyway afternoon session went smoother. Better pacing, more on time- 30 minutes/ question, except 5 took 1 hour, and I didn’t do 6. B4 was lovely, I’ll present it at problem solving seminar tomorrow.

After the test I lingered a bit, to hear others talk about how it was and contribute my comments. Though maybe I shouldn’t have. It still seems like bragging. Lingering around, waiting for others to ask so I could say I got 5 problems. It is bragging though. The pleasure of doing well- should really care about it less.

[…] Somehow after a math competition I get real talkative. […]

During dinner, before, I was thinking about my promise to myself not to take the Putnam next year. Or even ever again. After the Putnam this year, though, I seemed to be getting attracted to the math competition stuff more again. Like, I did moderately well (by many standards, extremely well for a freshman); if I could develop my skills more, I’d get even better over the next three years, have a shot at being Putnam fellow! It’s like being in 9th grade and making MOP- a future in USAMO/ Putnam ahead of you, why would you just turn away from it? I wasn’t in that boat in 9th grade, but I am now: in 2.5 years I’ve managed to catch up with the IMO folks in math problem-solving, and now stand as their equals in Putnam, in the higher tier, an exclusive club? This was exactly the direction I feared, and I’m renewing my promise to not take it next year. I’ll get more time to concentrate on my other math work. Isn’t sacrifice more meaningful if I have something to lose- I want to throw away my possible future at Putnam to make a statement that math competitions don’t matter.

I did wonder, sometimes whether I went down the right path at the crossroads, where I decided to become a math professor. It was partially by choice- by 10th grade I had pretty much stopped writing so I said I could “only” go down the road of a math professor. But of course it was also the magnetism of math competitions- when I started working so hard on math I had my career pretty much set. All this work toward math can only culminate in doing math research sometime in the distant future; no way I could just waste the effort. And of course, I liked math better after working so much on it. […] But it seems so sad that the creative part of me is closed off; all those story ideas that never flourished. I’m going to start writing this diary so maybe it will help my ideas flow better, and I could get back to actually writing stories sometime. I could spend a portion of my working time on writing, and that wouldn’t eat away at my math time to much, provided I budget my time a bit better. (Yes I need to do that, because despite what I tell myself I AM WASTING MUCH MORE TIME THAN I SHOULD BE WASTING!)

I got too much of the showing off my math bravado attitude- oh man I do math for fun, every day, spend 90% of my time on it, I do it when I’m eating, showering, walking, I know how to work hard and that brings me to success- and bragging-like. No, it’s okay to admit this isn’t true all the time. It’s okay to be more normal, not insanely passionate. The September issue of AMM had a really good article- “Mathematics without Passion”- I’m glad I read it, now I agree with it and see how I have been wrong to perpetuate this passion-bragging thing.

[…]

On the other hand, I do think I have a great responsibility. That’s a great quote from DAPER “With great intellect comes great responsibility.” I think that that because I am so good at math, I have a responsibility to “work harder.” Not to disgrace the people who may not have so brilliant a mind, but still work one-mindedly towards their life’s passion. Since I have a possibility of contributing to the body of knowledge of mathematics, I should always renew my efforts so I can do something of that sort. Sometimes this thought keeps me going when I don’t feel like doing math that much.

It’s really inverted from what it used to be. A huge perspective shift, in the positive direction. From working hard so I can succeed, so I can win and be better than everyone else (and self-righteously and silently brag about me deserving it after my hard work!), I’m working hard so I can contribute. (Some may argue that math is an extremely useless subject, what’s this about “contributing,” but that’s not the point here.) […]

When I think back to my USAMO days, and how much time I spent working on math, I always have a regret. It’s not that I spent so much time of math- I learned an incredible amount from my hard work. It’s the mindset I had when I approached the work. The mindset that my purpose of doing this is to win the USAMO, though of course my passion fueled me, it was just chemicals to keep me going. The idea that if I didn’t win, all of my efforts were wasted, because the goal I had when I was training wasn’t reached. And of course this thinking fails, especially since I didn’t win. The mindset that I was hanging in there so that I could win, God would not let it be otherwise considering how hard I worked! The idea that if I had known I wouldn’t win, all my hard work would be knocked flat because I wouldn’t have gone on like that knowing my purpose would not be fulfilled. The idea that I had been working towards a mirage for two years. […]

When I approach my work this way, I can’t get downhearted anymore. If I fail, it’s so I can learn from it. It’s not my success that matters. […] we all have to admit, it’s the thousands of people who continue to decide to go into mathematics (or another science) and spend their career on it, that keeps the train chugging forward. The communal contribution of everyone, the dedication of their minds. And no, not rated based on how many hours per day they spend on research. But the very fact that they are working towards a furthering of the subject. We all forget this. We talk about this, it’s a pity that so many people are unrecognized, etc., but often we really fail to appreciate the massive community effort, the large number of people sticks thrown into the fire. This is the true way to think of advancement of science.

1-5-10

“Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.
        Langlands, in Mathematicians: An Outer View of the Inner World, p142.

[…] Anyway I like the quote. It applies a lot. The more I compare myself to others, etc. the less I really like math, and the more time I spend just doing it, and not thinking of anything else, the more I like it. Though, this has the side effect of not allowing a diffusion of ideas. I hardly go on AoPS anymore. I find that I don’t actually learn that much searching forums for problems; I don’t know whether a random problem is a good problem, whether it applies to what I’m learning, etc. It’s too sparse and unrelated, the knowledge I would gain. I’d rather read a good textbook, front cover to back cover, and work on a large number of problems from one or two good problem books. I learn better that way (of course, everyone learns differently). Anyway one bad thing about me is that the more I interact with math sites online, the more I worry that I’m not learning fast enough, or working hard enough, or even interested in math enough, because there are so many other smart passionate people out there. This is bad; I shouldn’t think this way. So I mostly learn by myself. I’ll try to be more humble and learn what I can from other people’s sites. That’s a really nice thing for them to do. I really should make a blog too. After going through several cliché names (Journey, burst of insight, web of knowledge, explorations) I’ve decided to call it “Mental Wilderness”.

1-6-10

…it seems difficult to change human nature: I had an intensely competitive nature in high school, and while it’s less now, it’s still there.

3-9-10, Tue.

http://www.xkcd.com/610

[…]

Since I feel too dumb to write more Silfa today, I’ll put a list of some feelings that I don’t know how I’ll express in the story, but that I wish to express: (The major ones are easy. These are more complicated.)

  • The disconnect between other people’s perceptions of me, and what I perceive other people’s perception of me are. It’s easy to just criticize myself for my feelings and selfishness- and indeed I should have- but it’s also easy to overdo it. Like, I say, oh, I made a mess of math club. And probably some do think that. But […], for example was always a loyal friend, and he always thought pretty highly of me. And I might have bad feelings, but restraining them- preventing them from turning into actions- is also important. The difficult thing in writing Silfa is to avoid the tendency to exaggerate either way– turning Silfa into a wonderful leader or turning her into a mean, antisocial freak. It’s not black and white- gray is realistic. After high school, I felt like shouting to my friends, “Why have you been so nice to me? Why do you think I’m such a great person? Don’t you realize how selfish and conceited I am?”
  • The flitting back and forth between a fake certainty and self-doubt. Like, during high school, there are times when I’m caught in this euphoria, “I’m president of math club, I’ve improved so quickly over the past 2 years, I’ve learned how to work hard, I’m the model of success, I’ve been doing well on practice olympiads recently, of course I’ll win the USAMO!” and the doubts- do I need to say anything else?- I think I’ve explained that part in my essay before. The instability.
  • The inherent contradictions. Yes I work hard 90% of the time. But there’s also time when I have fun. And maybe I exaggerated the “working” part in my essay a bit. Also the fact that when someone ask me “Why are you doing math?” and I say “For fun,” when the correct answer is “For training.” Sometimes, possibly pretending, convincing myself that I like math more than I really do, as a show of bravado. Fooling myself, for better or worse, that there’s no better thing I would rather be doing other that tool on an olympiad. I need to project these feelings in Silfa, in a way so that the audience can see and understand both sides of the contradiction. This is really difficult, as Silfa is the main character and she would keep her feelings from herself as I would. It’s like a kind of twisted dramatic irony that the audience knows feelings Silfa has that she herself does not acknowledge.

 

3-20-10

[On getting honorable mention on Putnam]

How different this feels from USAMO in high school! I was happy. I didn’t care as much as I did in high school, but also it was that I was only in my freshman year of college. I was a bit too proud, I think.

I rethought about my promise not to take it next year. It would be so easy to go with the flow, train for Putnam the next three years, to be a winner… After some mental deliberation, I concluded that I could not break my promise to myself to abstain from Putnam next year. The years after that- we’ll see- though I still would like to not take it. Sacrifice is more meaningful when I have something to lose- an opportunity to win. I want to throw this opportunity away, as a kind of personal statement.

4-9-10

I looked at my plan for the rest of undergrad and found that (number of math classes)>>(number that a person could take during undergrad and stay sane). […] Anyway it’s always more fun to think about taking a lot of math classes and learning a lot of math in the future than actually tooling on that PSet in the here and now, for some reason (*laugh*)…

4-17-10

[On getting a good grade on the 2nd analysis test]

Anyway, my second thoughts were saying, This is bad. A score that’s near the top of the class even when I did pretty bad (failed) by my standards and didn’t study that much seems to say I can naturally do better than others and gravitate to the top even if I don’t try that much is not the correct message to send. I was prepared for the test to humble me and show that there’s a lot of work I need to do, but instead it’s going to feed into my pride? That’s very against the kind of message I stand for- The message that people who are naturally talented should not outperform those that are less so but more hardworking. But maybe it still works out, since I’ve worked hard already…?

[…]

This historian dude called Curtius analyzed why the West was more “successful” than the East, and basically his answer was, everything. But reasoned in a very logical and believable way. It’s because the people are better- their desire for challenges and struggles, compared to the Eastern peoples’ materialism. Even the geography of the land (mountainous terrain and sparse soil) contributed to the success of the West! People were thus forced to work hard that prevented indolence like that of those in the East. So logical yet so biased and so WRONG! In fact, these very ideas gave root to Hitler’s racism and his vision of an Aryan race. Be careful what you say!

This strikes a chord because often I think it’s easy to be too pretentious when one feels successful in life, and explains it in terms of the environmental conditions (challenges) and personal efforts. Take my constant discussions of math olympiad experience, for example. I had to struggle from being a failure at math competitions and fight my way to the top, unlike those people who were born smart and never had to work! Because of the mountainous terrain and sparse soil the people in the West are hardworking unlike the people of the East, who never have to work much and just enjoy their material wealth! Isn’t the resemblance striking? I don’t say stuff like this- though I’m sure I wrote something like that in my math experiences essay- because I’ve grown more and more aware of its negativism. Even saying my father’s death motivated me to work hard is on one hand inspiring but on the other, selfish. My proclivity for analyzing and finding a place for every detail (reinforced by the training on writing essays in high school!), like Curtius’s explanation for every detail, even turns weaknesses into strengths. [A friend] mentioned that it might be better not to focus just on one thing, that it would be better to broaden interests. I rebuked that by saying that some people might have multiple interests but I only have math. I kept being afraid that […] my statement was rude. It’s implicitly saying because of the way I am, I am better than others- because my association of one-minded determination with success was still too strong back then. [Since then, I’ve eaten my own words, because math hasn’t been the only thing I’ve been doing. I’ve realized that there’s other stuff I want to do, that I should do!- like writing stories. Not, of course, to degrade those people who do only have one interest. Both are fine, neither is better!] It’s reinforcing the stereotype that the only people who are “true” mathematicians are those who slave- who tool– their life away. And we all know this stereotype is reinforced in math clubs everywhere, on AoPS, at MIT.

Certainly it’s nice that I could turn challenges into progress, but I must learn to do so, and express my experiences in away that respects others, instead of just supporting own success like all ideas in an essay support one and only one central thesis. I’ve always thought about how fitting it is that the Buddhist club at MIT (more than elsewhere!) keeps emphasizing turning challenges into an opportunity for growth, and that we should seek challenges every second of our life.

(And yet, does this disrespect people who want nothing more than material comforts and possibly a few friends, and are satisfied with that, instead of looking for something challenges every day? Challenges every second is probably an exaggeration. There also has to be a message of a middle way! But the tricky thing is, a middle way or balance is different for every person. Some people have it geared more towards work, and some towards fun, but we must avoid saying that one is better that the other! On the other hand, it’s also bad to say that everyone should accept their own balance, because then someone who does 50-50 work-play might feel like they never can break out of that to achieve as much as 60-40 work-play. So yes, people can change their balance (like I did). However, then we run into the same problem as at the beginning, where we’ve seemed to have set up a one way street- you must work harder! Which is exactly what we didn’t want. I don’t know what’s the best way to say things; it’s almost like a hands-off approach is best: I can’t claim to speak for anyone but myself, everyone must find his/ her own meaning in life. In my opinion a balanced lifestyle is not defined as an optimal percentage of work, play, and socializing, but rather as a pattern of life sustainable for an extended period of time (say, years) that can be supported even in the light of unforeseen obstacles. Ex. Working on math for the sole purpose of competitions is not a balanced lifestyle.)

[A friend at Buddhist club]’s experience tells that really well- she says that she has impossible amounts of work to do, but she just always keeps the attitude that it’s helping her learn and grow, and do it. The challenge is how to use our own success to inspire others to lose inertia that they can’t escape from their current circumstances and believe that they have infinite potential, to challenge themselves. A success story in isolation can be a deterrent- that person is so hardworking, that person is unique, one in a million, I can’t hope to attain that level of determination or genius;- it has to transcend individual boundaries to give a humanistic hope for all. As [she] says, she works not primarily for personal gain, but so that her story can inspire others. Wow! That is noble. I must remind myself of this goal more often.

Man, I should write a book of essays or something. Analyzing everything and coming to the conclusion that I shouldn’t analyze anything. I never thought I would become an essayist.

4-28-10

I looked up Putnam results. Apparently I got less than 70 (I don’t know what exactly my score is). Which is totally off from my prediction of 81. What the heck?! I thought I solved 9 problems. So, maybe I got 8 points off on that quadratic residue problem. I definitely got 1 point off on that linear algebra problem, and possibly 1 point off on the group theory problem for forgetting to cite a theorem. That’s still 80. Maybe there was one problem which I thought I got completely right but got completely wrong? Maybe B5? That’s still 70. Maybe I got 1 more point off somewhere? OK, so 69-ish? Crap, I probably just missed the top 25. This brought back evil cycles of math competition thought. It’s been one year since USAMO… Man, I so want math competitions out of my life. The more impersonal, the worse. I wasn’t convinced before but I am so going to boycott Putnam next year and focus on schoolwork. If I had gotten the 9 problems written correctly I would have gotten 90, which is like, top 10. So I could very well get in the top 15 next year if I decide to take the Putnam, and not mess up writing my proofs. See, I hate myself for thinking things like this. Which is exactly why I’m NOT taking it next year. The amount of productivity wasted from thinking about my scores and all is astounding. One argument for me taking it is that it helps MIT win. But does it really matter that much? Besides, that’s just a stupid reason that the part of me who likes using math competitions to be better than others comes up with as an excuse to continue taking it.

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