Yiannis Fam: IMO 2017 Brazil Report
The 58th International Mathematical Olympiad was held and brilliantly run in Rio de Janeiro this year. The IMO is a mathematics competition bringing together talented teams from over a hundred countries to solve beautiful problems over two days of papers, each lasting 4.5 hours with three problems for each day. The six of us in the team - Andrew, Keiran, Tony, Stacey, William and myself - have been training hard over the past few months under the guidance of team leader Michael, deputy Robin, and manager Phil, to prepare for this prestigious competition. It was an honour not just to participate in the IMO and represent New Zealand, but to have worked through the training programme offered by the NZIMO, from camp to squad to team.
I've spent three hours in a state dangerously close to sleep. Our two taxis race to our hotel through the Brazilian night. The city is lit up beautifully and some of us get a glimpse of the Christ the Redeemer statue. Our driver arrives first. After solving an inequality with the number of beds, we sleep promptly. The beach view is fantastic.
We wake at 6:30 and do algebra. After breakfast (cheese bread) we visit Barra beach. The sky is clear and the beach view homogeneous. Islands appeared to converge in a ring around the city until we discovered a second ring further beyond at sea. We have a treasure hunt for Andrew’s sandals in the sand. William claims that the number of people selling plastic footballs and sunglasses is infinite. We are yet to establish that this number is in fact bounded above. We discuss a problem regarding two hikers climbing mountains over lunch (bread and cheese). An awful geometry problem and nice number theory keep some of us awake. The water pressure in the shower is best described as violent, and the temperature sinusoidal.
We move to the IMO hotel today and are introduced to our lovely guide Leticia. She takes us for lunch at a nearby cafe and our choice of food is bimodal. We return to our rooms to do geometry and algebra.
Today is the day of the opening ceremony. We greet the Australians at lunch, leave an excessive amount of souvenirs on their table and are koala’d (definition: to have a koala clipped to your clothes or elsewhere - nothing is off limits) in return. We listen to some speeches, hold our flag for a photo and stampede out the door. A wall has been set up for writing messages and was inevitably covered with strong opinions on both combinatorics and geometry. Geometry is of course vastly superior.
This exam was strange. Question 1 was unusually easy and question 2 ridiculously hard. Consequently the whole team were delighted at solving the first question quickly but made little headway on the functional equation question 2. Question 3 is statistically the hardest question in IMO history. We learn after the exam that almost all teams struggled with the paper and so feel a little better. We end the night with Foosball.
This exam was less strange. First question was geometry that was standard in difficulty followed by a hard combinatorics question which we again made little progress on. After the exam we try unsuccessfully to forget the maths and explore the nearby Village Mall. It is apparently designed for wealthy tourists and we cannot afford anything. We visit the Lego Museum where the art conveys some deep messages about the human condition - exceptional English essay material.
Coordination of our exams has begun and our leaders are hard at work holed up in a hotel away from us. Despite everything being out of our control we are nervous to hear news that several of us may lose a mark on question one. We travel to Sugarloaf mountain by taxi and take the cable car up. The British team await us at the top where they have enjoyed the view of Rio through a blanket of clouds. Said clouds disappear the moment we arrive and the British leave. The view is indeed spectacular with dramatic cliffs and rich, blue waters and the excursion was my highlight of the trip. Some brave souls ignored the cable car and climbed the mountain by hand (or perhaps they were too stingy to pay the fare). On return, we take a group photo with all 600 participants on the beach. This did not turn out at all as expected, that is to say, the organisers succeeded (hats off to them). Police close the road for us to cross. We feel falsely important.
Michael has done his job well as we do not lose marks on question 1, making this the first IMO where New Zealand has scored perfectly on two questions, a fantastic achievement for the team. Our marks on the remaining four questions are less exceptional and several of us (rather, all of us) are expected to lie within epsilon of medal cutoffs. Today is the official excursion and we visit the lagoon, Olympic boulevard and Maracana stadium. The street art at the boulevard was breathtaking but I was disappointed we didn't get to see more of the Olympic stadiums. Medal boundaries are released and they are disappointing but expected. We have three bronze medals and three honorable mentions which is still a tremendous result, placing us 46th from 111, our third best ever relative result. Four of us return to the beach to bury Andrew in the sand. Our treasure hunt gets more intense and sand starts to fly.
I wake up and bite down on sand grains. Today we went to see the Christ the Redeemer statue. We were worried about the thick clouds blanketing the hills, possibly a reflection of the mood of some, but again good luck was on our side and we had clear views the whole morning. Although it was crowded we still had the chance to take lots of photos and buy souvenirs. We arrive back in time for the closing ceremony. There are issues with the order of medal winners (and not just that we were not in the order requested by Sir Alex in question 5) but the rest of the ceremony proceeds smoothly. The Australians hold their flags both upside down and left to right. We go downstairs for the closing dinner - another Brazilian buffet - and enjoy the performance of a group of lively dancers in bright costumes. Michael does not win the Golden Microphone (awarded to the most vocal team leader - “quantity not quality”) which dampens our mood somewhat. More pictures ensue and we retire for the night. The absence of a nearby McDonald's means there is no chicken nugget party (that I am aware of).
The flight is long.
One of my most memorable moments from this event was the lecture given to us by Field Medallist and IMO gold medallist Artur Avila after the official excursion. Artur spoke of the opportunities available to us once we have ended our IMO career, in pursuing research mathematics and how one decides on the pathway they are to explore. It’s become clear to me that the IMO functions as the training wheels on a bike, in which it provides the platform and exposure for the critical thinking required at university level and beyond. The IMO has trained me to think deeply about mathematical problems, as they are less penetrable by the mechanical processes of high school maths and more focussed about intuition and creative thinking, and rewards beauty and elegance of solutions. Although Artur acknowledges that the problems one faces at IMO are vastly different from those in research mathematics, the skills in problem solving I have developed from training for this competition will greatly support me in my future studies.
Moreover, this competition has inspired me to pursue research mathematics as a career. I have enjoyed my training in solving curious, beautiful problems such that it has become more a hobby than work. There is something enchanting about working on problems that require deep thought over calculations which has drawn me to mathematics since I began my olympiad studies two years ago, and I am grateful to have discovered this early enough to grasp the opportunities presented to me. A common analogy is of the mathematician as a hiker, climbing from mountain to mountain, theorem to theorem, and from each peak one sees the path to follow and climbs on, ad infinitum. My training in math Olympiads has given me the chance to look away from the beaten path and explore the landscape around me, find the tracks yet unexplored and enjoy the glorious view surrounding me. From this I have developed my passion for the subject. I see this love of mathematics present in my fellow contestants and this helps us to bond and share our ideas. Not only will this benefit me personally as I move away from home to university, but also my mathematics as it helps me to build on the work of others and share my own ideas so we can climb together. I suppose we've “taken the path less travelled by, and that has made all the difference.”
From my experience in this Olympiad I've changed my perception of mathematics from the mechanical and competitive nature of high school, to the mathematics Artur Avila spoke of, of collaboration and deep, focussed thought. I've thoroughly enjoyed the time I've had to work with like minded people and this has accelerated my learning and expanded my problem solving skill base, as we share the skills and strategies unique to each of us. Participating in the IMO has taught me about how I can contribute in my own way to mathematics - how precious different viewpoints and ideas can be, and I believe this will give me the confidence I need to improve as a mathematician. So I'd like to thank everyone that made this experience possible - my team leaders and manager, the competition organisers and generous sponsors, particularly the Royal Society of New Zealand - for the opportunity to participate in this wonderful competition, and for instilling in me a passion for mathematics and teaching me how to think. Thank you too, to my fellow contestants for being such great friends and teammates, and I wish you all the best in your endeavors, and to those returning next year, I hope for an even greater result.