The team, from left to right: Emily, Seán, Fionn, Tianci, Yuan, and Owen.
The 64th International Mathematical Olympiad took place in Chiba, Japan, between the 2nd and the 13th of July, 2023. The Irish team were:
Fionn Kimber-O’Shea, 5th Year, Christian Brothers College, Cork
Tianci Yan, 3rd Year, Wesley College, Dublin
Emily Wolfe, 6th Year, Bruce College, Cork
Seán Hallissey, 6th Year, Clongowes Wood College SJ, Kildare
Yuan Li, 5th Year, Sandford Park School, Dublin
Owen Barron, 3rd Year, Coláiste an Spioraid Naoimh, Cork.
The Leader was Professor Mark Flanagan, and the Deputy Leader was Luke Gardiner. The team returned with an impressive haul: Fionn achieved a bronze medal with three perfect solutions to problems 1, 4, and 5, giving him the fourth-highest score an Irish team member has ever achieved at the contest, and Emily and Seán each came away with high-scoring honourable mentions, having perfectly solved problem 4 and problem 1, respectively. In general the team this year were very strong, and Mark and I were extremely impressed with everyone’s mathematical creativity, both during our pre-IMO training camp and in the actual exam.
The team met up in Dublin Airport at 6am on the 30th of June, ready to face into a 20-something-hour trip to Narita Airport in Chiba. Our seats were somewhat scattered on the short flight to Zürich, but we were grouped together on the longer leg from there to Narita. In spite of our rather early morning and the abundance of content on the in-flight entertainment screens, Yuan and Tianci were noticeably eager to talk about maths; they had the misfortune of being seated next to me, so I ended up explaining the Axiom of Choice to them. What else would one talk about on a 12-hour flight?
On the way from the airport to our hotel we met up with Taiga Murray, who had been on the team in 2021 and 2022. This involved us going via the busiest train station in the world, whose labyrinthine core we fortunately managed to skirt around. We arrived at the Hotel Cadenza Tokyo, where we were going to have our pre-IMO training camp until the arrival date for contestants at the main site (the 6th of July). As soon as we arrived, Mr. Kengaku, the hotel staff member responsible for us, very kindly accompanied us all the way to a nearby restaurant so we could get some lunch. The team jumped at the opportunity to try Japanese cuisine, with a number of them ordering an option which came with free refills of soba noodles. Upon arriving back at our hotel, still relatively fresh off a long flight on which not a lot of sleeping had happened, some of us said we would try to stay awake long enough to go for dinner that evening; ultimately, nobody managed this except Taiga, who had arrived in Japan a few days before the rest of us.
We began our training camp in earnest the following morning. Each day after breakfast we headed up to our meeting room for the morning session. This was followed by a lunch break, after which we would return to the hotel and begin the afternoon session, generally finishing our training at about 5 or 5:30 each day. In each session one of the three trainers (Mark, myself, and Taiga) would begin by presenting solutions to example problems or explaining some useful ideas, with interaction from the team members, and then hand out a problem sheet for the team to work on for the rest of the session. Mark gave the first three sessions, and then Taiga and I divided up the remaining six evenly between us.
The hotel was charming and extremely well-suited to our needs. The meeting room was perfectly set up for our three-hour training sessions, with a large whiteboard at the back of the room and some good table space. There were a number of other meeting rooms on the same floor, and there was always something else happening concurrently to our training; at one point, several of the rooms were being used for filming a TV show. The buffet restaurant on the ground floor where we got breakfast each morning had a mild Hawaiʻian theme, and because we were coming up to the Japanese festival of Tanabata there was an area next to the entrance of the restaurant where people could write wishes on little rectangular pieces of paper and hang them up on some bamboo, which some of the team did.
Our lunch breaks usually took the form of us walking through the “Spring Wind” park behind our hotel up to a convenience store close to the entrance to the larger Hikarigaoka Park, buying a selection of onigiri rice balls, sandwiches, etc. there, and sitting down at a stone table in that park, right beside a section where musicians came to practise their instruments. It was a lovely residential area, and it was extremely pleasant to be able to walk through those parks every day (the shade provided by the trees was very welcome too, considering that on some days the temperature went as high as 36°). We didn’t see many other non-Japanese people while we were there, and one day an elderly Japanese gentleman came over to ask us where we were from, and then told us that he was 85 years old and he was about to go to the gym. In part, he had been aiming to practise his English with us, but this was not the only feat of linguistics evident during our time in Japan: on one or two occasions, Fionn switched to Irish so as not to be understood by anyone around us, and Emily had a habit of peppering some French into her speech, just to add a certain je ne sais quoi to her sentences.
On the afternoon of the 5th, having deemed that the team had earned a bit of a break with their efforts during the training sessions, Taiga and I decided to bring them to Shinjuku, so that they could experience a bit of the heart of Tokyo. We took them to a game centre first - essentially an arcade that also has crane games etc. - so that they could try out the various rhythm games within, and behold the remarkable capabilities that some of the regular customers had at these games (Taiga himself was also obscenely impressive at Taiko no Tatsujin, a game operated by beating controllers shaped like taiko drums - more on those later - with real wooden sticks). We then headed around a variety of shops and took the team to see an enormous Godzilla statue, which, through sheer happenstance, started making noises from the original film just after we got there.
The following day we headed to the IMO site in Makuhari, Chiba, and checked in at the extraordinarily tall APA Hotel ＆ Resort Tokyo Bay Makuhari. There were a couple of signs in the street talking about the IMO, and the hotel itself was thronged with young mathematicians from all over the world. International socialisation began even before we got there, with the team running into the delegation from Kazakhstan on our way from the station to the hotel.
The opening ceremony was on the following day, the 7th. Each team went up on stage, accompanied by their guide holding a sign with the country’s name and flag on it. There was a particularly loud cheer for the Ukrainian team. Outside of this procession of countries, there were speeches from dignitaries and mathematicians, and two performances, one by a group called Wadaiko Arakawa Shachū, who played taiko drums, and one by an all-female brass band called Tokyo Brass Style, who earned a standing ovation.
The next day the teams sat the first paper in a large hall in the nearby Makuhari Messe convention centre. Problem 1 was a number theory question about divisors of a composite number, problem 2 a geometry question, and problem 3 a difficult question about polynomials and sequences of natural numbers. It was quite unusual for the “medium” problem on one of the days to be on geometry; one of our team members had been hoping for one of problem 1 or 4 (the “easier” problems) to be geometry, but alas, this was not to be; the second day’s paper contained an inequality for problem 4, a combinatorics problem about “Japanese triangles” for problem 5, and a remarkably difficult geometry problem for problem 6.
Having looked through each team member’s solution to each of the problems together with Mark, I can say that the team really did distinguish themselves in the exam; there were some very clever, extremely slick ideas on display, even in cases where this wasn’t necessarily represented by the final scores.
Kaminarimon Gate, at Sensōji Temple
While this work of looking at the scripts and deciding on final scores with the coordinators was going on, the team had two days of excursions: on the 10th, they went to Tokyo Disneyland, and on the 11th they went to the Skytree, Solamachi, and the iconic Sensōji Temple in Asakusa. This was the first time they were heading off without the Deputy Leader, but given that they were with our guide, Ayana Fuse, who had told us that she had already been to Disneyland a double-digit number of times this year alone, and that Seán is a veritable human compass, I figured they’d be fine. Our guide was apparently mildly horrified to see that the team were doing maths on the train on the 11th.
With the scores finalised, on the 12th we went to the closing ceremony, where Fionn, as a medalist, was going to be called up on stage. Through sheer serendipity, the t-shirts given to the contestants this year were a vivid green, and the ones given to the Leaders and Deputies were a striking orange, so Fionn went on stage as a human tricolour, wearing a white t-shirt and holding one arm through the sleeves of his own green IMO t-shirt and the other arm through the orange one he had borrowed from me. This made quite an impression on everyone at the ceremony.
After the ceremony, there was a party back at the hotel, featuring music played by a group called steAm, including a variant of the traditional Japanese Bon-Odori dance accompanied by an original piece, composed for the IMO, featuring bars whose lengths were prime numbers, arranged in ascending order. We took some photos of the whole team just outside the hall where the party was happening, and Owen rushed back inside to get dancing again as soon as we had finished.
We headed out early on the following morning, making it back to Dublin Airport late on the night of Thursday the 13th.
I’d like to extend my congratulations once again to everyone on the team, and to give special thanks to:
Taiga Murray, whose training sessions during our pre-IMO camp were invaluable;
Yui Shimazu, who found and booked the extremely suitable Hotel Cadenza Tokyo;
Mr. Kengaku from the Hotel Cadenza Tokyo staff, who was extremely helpful at all times, and ensured that we were well-stocked on water and snacks during our training sessions;
All of the organisers and staff at this year’s IMO.
Last but not the least, we are grateful to our sponsors the Mary Vesey fund at the Community Foundation of Ireland, who made the Japan training camp possible; the Department of Education for travel support; Susquehanna International Group (SIG) for support with the Irish Mathematical Olympiad activities.