Brian Zhao: IMO 2023 Report

The hall was vast and imposing. The concrete floor measured 60 by 100, with desks extending in all 4 directions, surrounded by thick concrete walls, rigid, indestructible. The metal canopy rose 20 meters into the air, turning the nervous chatter of 600 students into a muffled noise, which slowly died down as the announcer asked everyone to be seated. Several contestants dashed for the bathroom.

NZL6 wondered whether the tremor in the ground was a product of his sleep deprived mind, or another earthquake. NZL3 told him that they were instructed to keep writing in the event of a minor one. He couldn’t be sure whether that was a joke. He started imagining the canopy falling down in pieces, and him dropping down in cover below his desk, feeling secretly relieved of not having to use the pens above, tidily arranged to save a split second of time during the exam.

The announcer said the exam would start in 5 minutes. How long ago was that? NZL6 fixed his eyes onto the giant screen, visible from every corner, which was blank except for 5 black digits. He could sense his breath rising, his heart pounding, like a suspended rollercoaster moments before going down -

Your exam starts now. And the clock started counting.

T-3 days, Narita Airport

The plane shuddered as it touched the foreign ground. NZL6 closed his laptop with a sigh, having solved nothing but Angry Birds. In his mind were two sequences, and the voices of his friends:

Mock results: 770 710 700 771

Silver cut-offs: 22 19 25 24 24 19 29

Brian, silver

r u rdy to not disappoint your bestie and mom

This is your last year. Make it count.

NZL6 cleared border control without further thoughts (Good luck. Said the officer). As the night fell, he found himself standing awkwardly before a hotel desk, trying to comprehend the strange hieroglyphs. The hall was deserted except for what looked like another IMO team, as the hotel empties itself to accommodate for 618 contestants. The brightest minds. The future leaders.

New Zealand!

CRI4 ran down the corridors, having recognised two of the members from last year.

Maybe it wouldn’t be too bad after all. NZL6 thought.

T-2 days, Imperial Garden

Kiwis!

NLDC waved at the NZL team excitedly. In her words, NLD and NZL were “a match made in heaven”. She was a cheerful Chinese girl with the mind of a polymath, an 8-time Olympiad qualifier and a speaker of 5 languages. Her teammates stood smilingly besides her; each a head taller than the average NZL member. Neatly trimmed pine trees rose on both sides, pairing nicely with the grey bricks and soft white walls, which merge into two heavy gates not far behind, placed at a right angle to slow down the momentum of attackers.

The two teams strolled leisurely through the trails, while chatting excitedly about their experiences in Japan so far, or their visit to Akihabara soon, or the scorching weather, or the training camps. Of particular interest was a hill, which was a novelty to the Dutch team, who were used to going up to the beach. They stopped for photos at the top, where one could get a nice view of the garden. A green veil that the city noises could not penetrate. A surprisingly tranquil sea at the heart of the largest metropolis on the planet.

30 km away, the hotel was becoming alive with the voices from a hundred countries.

NZL6 knew he was in trouble.

The countdown only had 4 digits now, and he was still nowhere close to solving Q2. He had drawn 6 diagrams, proven 3 lemmas, then forgotten why he needed them in the first place. He tried to comfort himself with his solution for Q1, but wondered how many people would find it too easy to take more than an hour. This thought did not help. He could already hear the complaints from last year:

Only people from very weak countries couldn’t solve it.

Surely half of your team swept.

Despite all the adrenaline, NZL6 could feel the tiredness creeping up to his limbs, his head. His right hand ached uncomfortably, and his legs felt numb and useless. Up until last year geometry had been his least favourite topic, a problem approachable only by bash. He remembered the CHN team member that said he never used a compass. He regretted not knowing MMP, or getting better at complex.

But he also remembered his joy at reading EGMO. The intricate configurations, each connecting a dozen points; the lively projectives, jumping between lines and infinity. It was then that he saw the cyclic quadrilateral.

With 40 mins to spare, NZL6 started on a new page, and labelled it S1.

T-12 hours, Hotel Spa

NZL6 uncurled in the steaming pool, sensing the warmth in his bones. This was the only place where he did not feel his chest tighten whenever he thought about tomorrow. NZL3 sat a few metres away, awkwardly trying not to look down; LAT2 lied in an adjacent pool, with his arms open and eyes closed. They wished each other good luck. NZL6 never saw him again.

NZL6 remembered the time when he sat meditating in the centre of a quad in the hours before IMO2021. He sent his consciousness into the bricks and soil below him; then the quad, alive with a tree in each corner; then the whole school, then the abstract space where the legends resided: Fermat, Gauss, Euler … NZL6 now tried to replicate that feeling, hoping to reach, if not some long-dead mathematicians, then at least someone in the CHN team, who he enthusiastically applauded for at the opening ceremony; or his team leader, who surely knew all the answers. But the water was too hot, and he could not afford to stay for long.

He left for the showers, still not used to his public nakedness. But decency was the least of his concerns tonight.

NZL6 almost burst out laughing.

4 years of inequality in a row.

Even though he had grown fond of most topics that he detested at first, inequality was an entirely different matter. He had never solved a single inequality in contests. Even trivial ones like a Q2 in NZMO2 were ordeals that required the use of Lagrange multipliers.

Screw it. He sensed intuitively that there was a way to treat the whole thing like combinatorics, to solve it without using inequalities at all. I decide what gets put on my test. He could feel his confidence rising, his thoughts flying. Within an hour he had figured out how to solve the question.

Yet it was in his triumph that he made his fatal mistake. A step that was deemed trivial in his roughwork suddenly seemed impossible to write-up. He knew the answer was right around the corner. But 5 pages of convoluted explanations had gone by before he realised that he was getting nowhere. He raised his card for bathroom. Whole pages were crossed out and rewritten. Another 10 pages of deductions were produced until he was half-satisfied.

It wasn’t until 5 days later that he realised that this step could have been written in 3 lines.

2.5 hours had gone by without progress on the other questions, and NZL6 was utterly tired. To his delight, Q5 was a combi. Combinatorics will never be a problem for me …

He was wrong.

The combi main could not solve a combi.

T+3 days, hotel lounge

Origami, Mafia, Codename, Disneyland.

Anything to distract himself from the exam.

I will wear my Minnie Mouse ears on stage if I get a silver. He said to NZLL.

Wear them anyways. NZLL replied cheerfully. Is that condolence in his voice?

One night, the leaders and deputies were all gone, which could only mean one thing – the Final Jury Meeting. The lounge was busier than usual, with dozens of contestants distracting each other with talks about their trips, letting loose a few nervous laughter. Then the mood shifted, and the crowds tightened, and a whisper started, quickly turning into shouts:

18 25 32

Several people had started yelling, in elation or in agony. But NZL6 was oblivious to them. His heart began to fill with lead as he guessed his mark and result. Yet he still wanted to hear them from his team leader, whose confirmation would extinguish that last flicker of corrupted hope which burnt painfully in his head.

NZLL and NZLD were still at the meeting, but NZLB, having missed it, stayed in the lounge.

What did I get.

23.

It really wasn’t going to go up from there.

NZL6 nodded, then stood in silence, where he was joined by NZL3, screaming at the top of his lungs about the tyranny of 1 mark, pressing his head against NZL6 so hard that he nearly fell. NZL6 muttered something along the lines of I understand, too immersed in his own loss to be comforting. He thought of what he would say to his parents, or his study buddy who had been his motivation for the past 6 months, or his MIT friends, waiting for him, at a college he might never reach.

T+5 days, Auckland Airport

NZL6 wished this story was different.

He wished he could tell you that he solved Q5, tried Q3, got a silver, and had a chance for gold next year. He wished he had worked harder, started earlier, studied inequalities, and grinded more shortlists. He wished he had talked to more people, visited more places, and been nicer to his friends when they were down. He wished it was about accomplishment through hard work, or making lifelong friendship, or some important lessons about life.

Once you step out of this door, you will cease to be a member of the NZL team.

Perhaps it was about these things, in a way. Perhaps on a happier day, he would tell you about his late night parties with a dozen teams, or his adventure with NZL2 and 3 at an arcade, or how much he genuinely enjoyed every maths question. But his story had ended.

Appendix A: soundtrack – A Million Angles

Not sure if I support the message here (combi deserves respect) but this song is fire. Shout out to Isabella Zhu and Vivian Loh for writing the lyrics, and Isabella for letting me use it. Shout out to 2023Q2 for carrying my mark.

Instrumental: https://www.youtube.com/watch?v=3f2X_gIJ_u4

Draw the lines, angle chase
Geometry can’t be replaced
As the best subject.
Algebra and NT,
Combinatorics cannot beat,
Geometry respect.

They can say they can say it all sounds crazy
They can say they can say I've lost my mind
I don't care I don't care if it's A, N or C
Everyone should just do geometry.

'Cause every night I lie in bed
Synthetic geo fills my head
Geometry is keeping me awake
I think of what the world could be
If there was just geometry
Geometry on the tests we’re gonna take
Oh geometry, makes the world a better place

Never bash, don’t use trig.
Only use classic configs.
And I’m almost done.
Configs give, deja vu.
Solved an ISL G2.
Geo is so much fun.

They can say they can say it all sounds crazy
They can say they can say we've lost our minds
I don't care I don't care if it's A, N or C
Everyone should just do geometry.

'Cause every night I lie in bed
Synthetic geo fills my head
Geometry is keeping me awake
I think of what the world could be
If there was just geometry
Geometry on the tests we’re gonna take
Oh geometry, makes the world a better place

There might be alg, and some NT
I want only geometry
On the TST

I may be right, I may be wrong
I'll probably get swept by it all
Days 1, 2 and 3
But the circle that I will invert,
Becomes a line, invert

'Cause every night I lie in bed
Synthetic geo fills my head
Geometry is keeping me awake
I think of what the world could be
If there was just geometry
Geometry on the tests we’re gonna take
Oh geometry, makes the world a better place

Appendix B: additional photos

Appendix C: Q&A’s

Q: How has attending this event demonstrated greater knowledge of available career paths in science and technology?

A: I would like to thank our sponsor Jane Street for making this event possible. Jane Street is a quantitative trading firm that works at the edge of what's possible, combining techniques from machine learning, distributed systems, programmable hardware, and statistics to trade on markets around the world -

Q: Has attending this event changed how you feel about science or technology?

A: No. I have always loved maths consistently.

Q: Now that you have had time to reflect about your experience, what have you learnt about yourself?

A: That I can actually solve geometry and inequality, but suck at combi.

Q: How has attending this event enthused or inspired you to pursue science and technology careers?

A: It has enthused me to help more people with Maths Olympiad. I would like to train the next silver and gold medalists, as a way to make up for my own failure. The lack of diversity at the IMO also inspired me to make the Olympiad more inclusive. I am currently working to improve Burkina Faso’s training program, after befriending their deputy leader at a summer camp after the IMO.

Q: What did you enjoy about your experience?

A: The best thing about the IMO was without a question the people there. I hope you could see how crazily smart and kind they were, despite being at one of the most competitive events in the world. Many people would ask me about my day, wish me good luck, express their congratulations or condolences, despite having never seen me before, and probably wouldn’t see me again. And there were the friends I made, who were simply the most awesome people ever.