# Keiran Lewellen: IMO 2016 Hong Kong Report

I have been working on competition maths for the past three years, and I am thrilled to have made it to the IMO team for New Zealand this year. Competition maths, unlike the maths taught in schools, does not focus on content or repetition but rather on solving new problems, different in type to every problem you have seen before. Most people think of the arts as where creativity is needed, and that maths and sciences require nothing more than hard study; however, true mathematics requires creative inspiration. Hilbert, one of the greatest mathematicians of the 20th century, was once told that one of his students quit maths to become a poet, and his reply was “Good, he did not have enough imagination to become a mathematician.” Competition maths teaches those who study it to think creatively about unusual and unexpected problems, and it helps students to see the underlying beauty in mathematics and that mathematics can be applied creatively to real life problems.

The 57th International Mathematical Olympiad was held in Hong Kong this year. It is a two day exam containing 3 problems each day to be solved over 4 ½ hours. Each problem is worth 7 points, earned by proving your answer and writing up a detailed and systematic multi-page proof. Before the IMO began, we gathered in Auckland for a five day training camp where we took four practice IMO one-day exams and listened to lectures on maths. The Wellington students, including me, were kindly hosted by the Auckland team member families. I did considerably better on these practise exams than I was expecting, scoring 7, 8, 1, and 7 making it clear to me that it was likely that I could get the first problem on each day. Although there are three problems on each of the two days, the last two problems are very difficult and only a half of the students who attend the IMO can get even partial points. This increased my confidence in my abilities as I was expecting to only rarely get the first problem. That Friday, we flew to Hong Kong.

After a long 12 hour flight, I arrived bleary eyed at the Hong Kong airport. To my surprise, there was a special booth set up just outside the arrival section for IMO attendees to register and find their guides. The multitude of banners in the airport celebrating that Hong Kong was hosting the IMO made me really realise that this was an international event of some importance. Once I stepped out of the air-conditioned airport, however, the hot and humid climate assaulted me. I was relieved to board our well air-conditioned bus which took us to the university campus where the IMO was being held.

The Hong Kong University of Science and Technology is beautiful. It is built into the side of a steep mountain overlooking part of the harbour. It has grand public spaces and an interesting network of enclosed bridges linking consecutive buildings. My room had a nice view of the harbour. Over the course of the IMO, I met many people from different countries especially Australia, Canada, and America, but also some people from Bangladesh and South Korea.

The exam itself was quite difficult, and in my mind it seemed harder than the mocks we had taken. On the first day I completely solved a problem, but then found that I missed a very small case, earning 6 points. However, I was pleased to earn 1 point on the second problem. The next day did not go quite as well. I made an early tiny arithmetic error which cost me an hour later on as I worked to find it. This left me rushed to write up my solutions, so I was forced to skip some case work which I thought was pretty obvious. Unfortunately, the markers disagreed, so I only earned a 4 out of seven points. Thus, although I only earned an 11, I felt that I was very close to earning two 7s and a 1, making a 15 -- one point off a bronze. As a 15-year old, I still have two more years left to possibly compete in the IMO, so my goal this upcoming year is to focus on solving more difficult problems, and by next year I think solving the first and second problem each day should not be very hard. I am looking forward to competing in future IMOs.

I want to thank Stephen Mackereth for spending an inordinate amount of time training the team. I feel like in the few months before the IMO I went from likely getting a 1 to getting an 11, and this is due to his effort and dedication. I would also like to thank Phil Truesdale for doing all the organization for our trip, and for being available in Hong Kong to answer questions and solve any problems that arose. Finally, I want to thank Michael Albert for helping me with test taking skills for the IMO and teaching me combinatorics. I know that this trip was very expensive, and I appreciate The Royal Society of New Zealand for sponsoring us and making it possible for me to compete internationally in mathematics. Making the IMO team has represented the ultimate goal which has driven me to develop my problem solving skills for years. The IMO in Hong Kong increased my confidence that I can compete in mathematics on the world stage.