Monday 5th October 2020

Phillip Han: IMO 2020 Report

This September, I had the opportunity and privilege to represent New Zealand at the 61st International Mathematical Olympiad(IMO) along with five other brilliant young mathematicians. Despite the Covid epidemic that has halted a multitude of programs, we were very fortunate that the IMO was able to continue amid cancellations to various other Olympiads. The IMO, this year, was postponed two months to late September this year in hopes of relative worldwide recovery and Russian hosting, however this was not to be the case and instead we were left with a virtual IMO with a number of countries unfortunately having to pull out including India and Egypt due to the need for certain rules and regulations that would help simulate and ensure a similar exam condition to that of a normal IMO.

We were fortunate enough to compete in the Cyberspace Mathematical Competition(CMC) in mid-July around the time of what would have been the 61st IMO. The CMC afforded me a unique opportunity to get to not only meet the Dutch IMO team this year but also take 4 mocks in conjunction with the Dutch that provided me with my first five hour exam. The windmill time with the Dutch has been a highlight this year and the numerous hours spent playing hanabi with my teammates as well as bombparty with the Dutch have been priceless. The actual CMC was not so much to my liking. While the problems were nice, the abundance of combinatorics(or combi as many of us would say) was rather disheartening for me. While I enjoy combi and the often graceful solutions that it provides, my lack of affinity for combi often leaves me at a disadvantage when compared to the other quadrants of Olympiad Maths. Moving on to the actual IMO now since I’ve taken up a lot of your reading about something you probably don’t care much about. (Note: we also went through a bunch more mocks and trainings, some of which were in conjunction with the Australians but I figured you’re already bored to death by my narration of the CMC that I may as well move on to the IMO)

We started our pre-IMO training on Friday 18 September. Incidentally, this also happens to be the day after a gruelling ten days of Term 3 Mocks in preparation for school exams. This leaves me with just a few days to forget all about my exams from the previous two weeks and get back into the groove of maths. I take the NZMO2 at Kings that afternoon with an assortment of Kings and Grammar students. We’re still under embargo at this point so I won’t comment on how I thought I did. The next day, Rick and Nathaniel and I decide to get together to do some maths before the IMO on Monday and Tuesday night. Rick proceeds to give us a functional equation on which myself and Nat waste a good few hours on before eventually giving up after being hungry and unwilling to leave a problem unsolved this close to the IMO. We then go and get food at Subway before heading home after an afternoon of maths to get ready for our final mock before the IMO later that night. I find the mock quite standard. Problem one is standard algebra that I get after around two hours. I’d wasted my first hour trying silly ideas and only once inspiration strikes do I realise how simple the problem is and it only takes me twenty minutes to hammer out the finer details before I proceed to spend a good fourty minutes writing out a winding proof. Problem 2 leaves me in the lurch as a medium geometry. I try a little bit of trigonometry and get very little before I proceed to stare at it for the rest of the exam and making no progress whatsoever. We have the opening ceremony Sunday night and the animations as well as good narration make it an exciting event. The enthusiasm of the host, a Russian reporter, and the well-choreographed event made for an exciting watch.

By the time Monday night rolls around, I’m actually rather nervous waiting for the IMO to start. However, by the time we get seated and have gone through all the procedures of setting up the cameras, I am left not at all nervous and just excited to get stuck into Day 1. I am initially delighted when I see problem 1 being geometry because I preferred p1 geometry over p2 or p3 geometry. Despite this, the problem had an odd angle condition that I am left unable to make sense off and this results in me spending most of the four and a half hours staring at one problem trying to make something off it. Problem 2 was an inequality and quite a surprise to me. No-one had been expecting an inequality this year and I certainly hadn’t practiced inequalities for quite some time, this immediately put me off p2 and resulted in me spending a good 4 hours on p1 only to get no substantial progress. I come out of the first day a little disheartened and disappointed in myself having not solved p1. Rick tells me that when he didn’t get anything last year on day 1, day 2 became much more relaxed and he got 4 and 5 the next day which was some degree of consolation at least. Come Day 2 and I’m just as Rick told me I’d be, not at all nervous and without any pressure. I manage to get problem 4 quite quickly before realising I’d fakesolved, this gives me a slight panic because a fakesolve could result in me spending the rest of the exam trying to fix my mistake. Fortunately, I am able to rectify my mistake quite quickly and with two hours left am able to turn my attention to problem 5. Problem 5 turns out to be somewhat difficult number theory and I make very little progress in the two hours I have left which culminated in my receiving one point for it. I was honestly quite happy with my honourable mention having gone into the IMO declaring that I’d be happy with an HM. However, a small part of me laments that if only I’d solved problem 1 which was very simple and statistically wise the easiest problem this year, by quite some margin, I would have gotten a bronze medal. Overall, I am still happy with my performance and thoroughly enjoyed the various interviews that were on offer as part of the post-IMO activities including interviews with Lisa Sauermann, Four time gold medallist at the IMO, and Grant Sanderson(3b1b). This has been a priceless experience for me, and I wholly encourage everyone who ever has the opportunity to make the IMO team to take this chance without hesitation.

I would like to thank all of the support that the Royal Society of New Zealand and the New Zealand Mathematics Enrichment Trust offers to not only the team when we do normally travel but also the various mathematical events that it helps run. The NZMOC, their monthly workshops and Maths Olympiad Program have offered me a platform in which I have been able to further my mathematical ability as well as meet other budding young mathematicians and I am very grateful for those opportunities. Finally, a huge thank you to Ross, Josie and May as well as the multitude of volunteers who have given up their time and effort to help train us and make this year’s IMO possible amid such a difficult time.