As I was looking through some of my Word files on my computer, seeing if I could find any that were no longer needed to free up some space so that my computer wouldnt hang as frequently as it does at present, I found an essay that I had written at the start of this year. It was compulsory for everybody in class to write an essay, and the 2 best entries would be selected to be submitted for the Commonwealth Essay Writing Competition. My essay wasnt selected, but I got 35/40 for it, and the best mark in class was 36/40. However, Ill say that it is extremely far from being of a great standard. Anyway, Im posting it here to find out your opinions on the situation I wrote about in my essay, because although it is totally imaginary, parts of it are based on experience I have had from being in the Singapore International Mathematical Olympiad Senior Team (not national training team), and Ive come to realise how much going to the IMO means to the national training team students. Here it is, and I want to apologise for the length of it, because I dont think I should make you all endure the torture of having to read so much in a single post. Your opinions are greatly appreciated.
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        Silence. Deafening silence. There was of course the occasional cussing, the scratching sound of pencils on paper, and the heavy breathing sign of nervousness, but other than that an eerie silence rocked the room.
        Calisto tentatively glanced around the room. It was medium-sized, with many rectangular tables arranged neatly in three straight columns. The lecturer sat in front supervising, not really paying attention, more engrossed in marking, knowing very well that his students had the moral honesty and integrity not to cheat.
        Next to her there was Davin. Strange as it seemed, they were the only people taking the test a four and a half hour long test with only three questions.
        Calisto found it hard to resist the temptation to laugh at it. Others might take one look at the situation and say that it was ridiculous, but she was perfectly serious about it. Davin and her were taking a tie-breaker test which would decide the ultimate whoever had more marks would get to go to the International Mathematical Olympiad, along with five other students from their country. It meant so much to both of them to go, because this was their final chance, as they were both in their second year in junior college.
        Twice Calisto had been lucky. The first time, at the selection for the national training team, she barely made the team cut-off point by one mark. The second time, at the selection for who would get to go to the Olympiad, she was sure that she was out except that Davin had been careless and got one mark less than he should have. She? Lucky. In the nick of time she had scribbled down an answer just enough for her to tie in joint-sixth place with Davin.
        It was the third testwould she be third time lucky? Briefly she glanced at Davin again. Smart, talented, with a natural aptitude for number theory, inequalities and combinatorics, an extremely promising student who looked set to surpass even his favourite mathematician, Niels Henrik Abel, he sure looked as though he had the answer for that final question that was just out of her grasp. Then she heard a confirmation.
        Eureka! he said softly, with a wry smile at her.
        Calisto tried hard to force a smile in return, but in her heart it stung and tore at her heartstrings. Six years of training all down the drain? She looked back at her question paper and tried hard to fight back the tears that were threatening to show any moment successfully.
        This was the third time. Now, the third time, she was not so lucky. When Calisto handed up the paper, she knew in her heart what the results would be.
        Congrats, Davin, she said with all sincerity. Have a good time in the US. The next Olympiad was to be held in the United States of America.
        Thanks, Davin answered, a smile from ear to ear. You are good too only you never believed in yourself enough, he added with a touch of seriousness in his voice.
*
        Calisto was deep in thought, muttering at herself in disappointment. It was harder to bear than she thought, even after a few days. So near, yet so farnow only did she understand how characters in stories felt. Before it always seemed to her that they were overreacting, taking things too seriously, but now she knew how they felt.
        Just then, the telephone rang, interrupting her train of thoughts. With reluctance, she picked it up.
        Hello?
        Calisto? Is that you? It was her lecturer. I dont know how to say this, but the voice of her lecturer trailed off, hesitation obvious. Davin has a high fever, hes in hospitaland he may not get to go to the IMO. So you might. The doctor says that he probably put too much pressure on himself. I spoke to his mother, she says he said up to two oclock in the morning to go through the proofs of the theorem of Stewart, the Simpson line, the relationship between the orthocenter, incentre and circumcentre and other stuff. Gosh, that silly boy
        Calisto immediately knew the implications of what the lecturer meant. It was simply that Davin might not have sufficiently recovered, and going off too soon might worsen his condition, which they were all not willing to risk. Psychologically also they were worried that Davin might be unable to take the pressure. Throughout the rest of the telephone call a single thought kept recurring in her mind, Maybe, just maybe, I can get to go to the IMO?
*
        It was obvious that many of Davins friends had also visited him at the hospital by the time Calisto went. Davin appeared fine, although he had not fully recovered, but Calisto was aware that staying awake to talk to them, albeit just a little, was taking its toll on him.
        After a brief chat, Davin told Calisto, Good luck at the IMO.
        For a moment Calisto was stunned, then it sunk into her. Recalling what Davin had said to her earlier, she replied, No, its just that you dont believe in yourself enough that you will be going. Youre worried that youll let us down. You wont, though.
        A wistful smile appeared on Davins face. I wish, he murmured. Then he presented Calisto a straightforward statement, the one thing she knew better than anything else, You want to go to the IMO. Heres your chance. Think about it. As an afterthought he added, Youre right. Im worried that Ill let you all down.
        The irony of the situation stung Calisto. Davin was better than her, he had done better than she had, and now he could not go she was going to. It must have been so disappointing for him to think about it
        At home, Calisto severely questioned herself. Yes, she wanted to go, but no, she should not, because Davin deserved to, and she was sure he would recover sufficiently to go. Besides, this was his last year a final opportunity, and he was admittedly better than her. Yet now the lecturer was giving her the choice. Silently in her heart she wished it was not so, perhaps if she had been third time lucky she would not have to make this heartrending decision.
        Yet her final decision was firm Davin had earned the right to go, and she was not going to take his dream away from him, no matter the circumstances.
*
        Two days after the Olympiad examinations, the results were released. Yet nothing really prepared Calisto for Davins result it would stun everybody. Forty-one marks out of forty-two just short of perfection, earning his country the first ever gold medal they achieved at the Olympiad. In that moment, she knew that she had made the right decision. This was something that she would never achieve, even in her wildest dreams, she knew. It had been right to give up a dream that she had been chasing for six years for this.
        As Calisto silently thought about it, slowly absorbing the rush of thoughts that came to her mind, she realised that she had been lucky. Perhaps not lucky enough to be able to fulfil her dream, but those two lucky times earlier on had brought her more. Medals were of secondary importance, the magic lay in the friendships made at training, and the friendship with Davin that she had now.
**
Quote:
Medals are of secondary importance, the magic lies in the ambience.
Tan Swee Heng, SIMO X-Man 93, 94.
Quote:
Proof is the idol before which the pure mathematician tortures himself.
Sir Arthur Eddington
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        A bit on the background of these 2 characters:
        At this point I would like to say that this essay was written in Calistos point-of-view. The way I, as the author, see it and intend it to be, Calisto is actually better than she thinks she is. She feels that she was lucky to get past the first 2 rounds of the selection test, however she actually has the capability in her to perform that well, and should have been in the IMO team if only she had more experience to bring out the gut feeling of solving problems.
        Davin, as I have specified so in the essay, is a very talented boy who truly has great potential to excel in future, to be an ace in combinatorics. He is an extremely hardworking student who is willing to stay up late in the night to have more experience at solving questions.
        Between the two of them, I would say that they are actually pretty well matched, Calisto being a bit more balanced than Davin, especially when it comes to solving geometry problems, which Davin is weaker at (remember however that it is in comparison to his strengths). I dont think you noticed it, but the topics which Davin stays up late at night to work on (the theorem of Stewart, the Simpson line, the relationship between the orthocenter, incentre and circumcentre etc.) are all geometry topics. However Davin is truly the master when it comes to combinatorics and inequalities. Overall I would say that Davin has a little bit of an edge over Calisto as he has more of a gut feeling of what to use to solve problems and has a bit more experience.
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        Thus, at this point, I would like to ask you all the following questions:
1. Do you agree with Calistos decision to let Davin participate in the IMO, instead of participating herself? In the essay, I focused on Calistos view that Davin had earned the right to go, however I would like you to think not only about that, but also other factors like he was not exactly at his best of health at that time and had great pressure on him to perform well, as well as whether it would have been technically better for the countrys probability of doing well if Calisto had gone instead. At this point, assume that the examination has not been taken yet, but Calisto has informed the lecturer of her final decision already.
2. Personally, if you were Calisto, what would you have done? It doesnt have to follow up to your response for question 1, you can be selfish if you want, but what would you truly have done?
3. Do you think Calistos thoughts at the end, that she has been lucky, and that medals are of secondary importance; the magic lies in the friendships made at training, and the friendship with Davin that she has now are an accurate reflection of her throughout the essay? Do you agree with what is being said, or do you think that she is merely fooling herself, that she would have done well also if she had been given the chance to go?
And finally, feel free to critique the essay and give any other comments that you may have. Thank you very much.
P.S. Kida, this is my first topic here, so if its in the wrong forum, feel free to move it, OK? :)

