IMO 2021 — Results and Analysis

The 2021 International Mathematical Olympiad was one of the toughest in history.

China showed once again that they are the undisputed world leaders in Olympiad Mathematics.

Special congratulations to Israel for achieving their first top 10 placing, Canada for its equal highest ever ranking, and Italy for repeating its impressive performance from last year.

Gold medals

Each IMO participant attempts 6 questions worth 7 marks each, giving a maximum possible total of 42 marks. Gold medals are awarded to approximately the top 8% of participants.

The map below shows the distribution of this year’s 52 gold medallists.

Hover / tap on bubbles to see participant names and scores.

One thing that surprised me from looking at the official statistics was the fact that the gold medal mark boundary this year was so low.

The fact that the gold medal cut-off was so low this year indicates that the 2021 IMO was extremely challenging, even by its own standards.

The COVID-19 pandemic no doubt played its part. Most teams were forced to move their training camps online. And as we all have learnt, there is something about physical presence which cannot be captured over Zoom.

Question Difficulty

Looking at the question-by-question statistics also reveals something interesting.

The surprising difficulty of Problem 2 is blatantly obvious. There has been a trend in recent years for Problems 3 and 6 to be exceedingly hard. But proving this inequality in Problem 2 was clearly unexpected and unwelcome.

According to the Art of Problem Solving wiki, this problem was proposed by Calvin Deng from Canada. The wiki also contains links to a video solution and discussion of the problem.

All countries

The scatter plot below shows each country’s performance in 2021, relative to their historical average.

Hover / tap on the bubbles to display country names.

Countries above the diagonal line performed better in 2021 than they have in previous IMO competitions. Philippines, Mongolia, Indonesia, Mexico and Saudi Arabia deserve a special mention for significantly outperforming their past results in 2021.

Finally, I want to give a big clap 👏 , fist pump 🤛 and “Hoorah!” 🥳 for all the IMO participants and Team Leaders. I am in awe of your ability and dedication. Keep pursuing your love of mathematics and sharing it with others 🙏.