Dirk Basson emphasizes that even though mathematics Olympiads are competitions, preparation often involves teamwork and that this social aspect of the competition makes the experience of participating enjoyable.
I have been involved in Mathematics Olympiads for most of my life. Throughout high school I was a contestant and since then I have been involved in training our national teams.
A Mathematical Olympiad is inherently a competition. However, many former contestants look back with fond memories, not to the competition itself, but to the interactions with other like-minded students, and to the “beauty” of the mathematics they encountered. For example, Po-Shen Loh, the USA Team Leader to the International Mathematical Olympiad (IMO) 2014-2019 recounts his own experience in the Mathcounts training program in the USA in an interview with ArtOfProblemSolving.org : “…what really sucked me in was that there were a lot of us who were working together as part of a team. Of course, it was competitive, but inside our room, it was extremely supportive.” Paradoxically, Olympiad contestants seem to experience a greater degree of collaboration than high school learners who do not participate in Olympiads.
Collaboration is an important part of training for the International Mathematics Olympiad (IMO). At the IMO students get 4.5 hours to solve three problems. It therefore takes patience, perseverance, systematic problem-solving, a deep knowledge and understanding of various branches of elementary mathematics, and sometimes a bit of creativity to solve even one of the three problems. In training, contestants are given previous IMO problems to work on and it sometimes takes weeks or even months to come up with the right idea. This can be rather disheartening if you are working alone for many months but becomes a valuable experience if it is interspersed with interactions with others going through the same process.
Unfortunately, funding and expertise to participate in mathematics Olympiads are limited. This means that the experience is limited to those contestants who place at the very top of various competitions. In other words, if you are already doing well at Olympiad style problems, then you are invited to a camp where you can experience this collaborative atmosphere. It would be great if there was a way to expose more learners to such an atmosphere at an earlier age.
There are a few initiatives that make this kind of training available to more learners. The University of Cape Town hosts a weekly Math Circle, Stellenbosch University has similar classes on Friday afternoons, and the South African Mathematics Foundation started the Siyanqoba programme and oversee the annual South African Mathematics Team Competition. In the latter, one of the papers is written by a team of ten learners who collaborate on solving ten difficult problems. But the most encouraging aspect of the initiative is not the competition; but rather the atmosphere created by dozens (or sometimes hundreds) of learners getting together because they enjoy solving mathematical problems.
A mathematical Olympiad is inherently a competition, but one may argue that learners enjoy it largely due to its social aspect: comparing ideas, learning from each other, and most of all enjoying the process.
Dr. Dirk Basson
Department of Mathematics,
 AfterMath: Interviews with the Best Minds in STEM – Taking Math Education to the Next Level, with Po-Shen (2 January 2019) https://artofproblemsolving.com/news/aftermath/taking-math-education-to-the-next-level-with-po-shen-loh