Teenage kicks

You're on your own kid, you always have been

With the Olympic Games starting in Paris this week, I’ve been thinking back to my own time participating in these kinds of competitions. Unsurprisingly perhaps, this wasn’t any kind of sporting contest. More in the spirit of the arts competitions that used to form part of the modern games, I was in the UK team for the International Mathematics Olympiad in 1991 and 1992.

For those that don’t know, the IMO takes place every year in a different host nation. It’s a maths competition for high school children, with countries entering a team of six. You can perhaps guess what the experience feels like, in terms of a collection of young and nerdy people placed under stressful conditions of competition - if not, then the movie X+Y is on Amazon Prime and the maths parts of that are fairly realistic at least.

The IMO logo from the 1991 competition in Sweden, depicting a Koch snowflake, which isn’t something to do with right-wing politics in America, but rather one of the first fractals, invented by a Swedish mathematician.

Competitors sit two exams on consecutive days, each with only three questions but lasting for four-and-a-half hours (!). Each country’s individual competitors’ scores are added together to provide an overall ranking. Each question is marked out of seven, so a candidate scoring top marks will win a score of 42 and a gold medal.

I didn’t manage that. Nor was I even particularly close. The marks are on the record if you want to look them up, but one year I got an “honourable mention”, the second I got a bronze medal (as awarded to about a quarter of competitors - I was about halfway down the full list of marks I guess).

Overall, I’m glad I did it, but also I have misgivings about the whole Olympiad system and process. Of course, I’m really proud to have come through the selection rounds and made the UK team. But the things I really remember about the experience are the social side of things - meeting people from around the world, and being a guest in the country (I seem to remember we got shown round the Kremlin and had tickets to the Moscow State Circus, and it was pretty cool sitting exams in the famous Moscow State University where Kolmogorov and so many others had worked).

The IMO has been taking place in the UK this week (having moved from Ukraine), and I’m sure all the participants have enjoyed visiting Bath. All of this requires a huge effort from volunteers to host teams, set and mark questions and so on, and it’s great that people are prepared to step up and do that. And in a purely patriotic sense, it’s nice to see that by coming sixth the UK managed one of its best positions in the last forty years.

From a mathematical point of view though, I’m less sure about the whole thing. You can find lists of old IMO problems online, and depending on how technical you are they may not mean much to you, but the key thing is to note that the questions can be quite stereotypical in nature. In particular, since the Olympiad grew out of Soviet-era competitions, there is always a geometry problem (or two!) of a style that was common in the Eastern Bloc in the 1950s and 60s. It’s far from obvious to me that given hundreds of smart young people in the 2020s, we should be asking them to solve a style of problem just because they were part of the curriculum under Khrushchev!

Further, there’s a certain unofficial curriculum of “tricks”. Some countries take the competition more seriously than others, but the ones that do well (China, USA, historically Russia/USSR) have done so by training their teams intensely for weeks and months at a time. I’m unconvinced that this is a good thing to do, from the point of view of developing young mathematicians. It reminds me a lot of the level I reached in chess, where to get any better I was going to have to spend hours learning books of openings by heart - this was more or less the time I stopped playing! Certainly there is benefit to studying and discipline, but it feels a little bit like getting the National Youth Orchestra together but judging them on the quality of their scale playing.

Maybe this is based on a Flanders and Swann mentality

they practise beforehand, which ruins the fun!

but it’s striking to me that there’s not a particularly strong match between countries doing well at the the Olympiad and countries winning a Fields Medal for example. China tops all the all-time IMO medals table despite only joining later than some countries, but are not strongly represented on the Fields list. Meanwhile France is 20th in the IMO medals table, yet has punched far above its weight in the latter category.

Some Fields Medallists did compete in the Maths Olympiad. But many of my former IMO teammates are not working as university research mathematicians now, and many Fields Medallists did not succeed through the IMO system. For example, the Quanta profile of Hugo Duminil-Copin describes how he “bombed” out of Olympiad selection.

Of course as a predictor, it’s much more likely that an Olympiad competitor will go on to that level of career success than it is for a random member of the population. A rough analogy is that some of the England team which won the under-17 World Cup in 2017 also played in Euro 2024, but many did not. It’s not really a surprise: the ability to solve quite stereotyped problems in an hour and a half is not exactly the same as the ability to do great mathematical research.

Indeed, modern mathematics is generally collaborative, not competitive. People work together over many years to solve problems, rather than racing individually against the clock - the description of how recent ground-breaking progress was achieved on the Geometric Langlands Conjecture is not at all atypical. I’ve described before some of what mathematical research consists of, and as I mentioned there:

I’d been thinking on and off about that problem for something like 12 years when we figured it out

It’s a far cry from solving three problems in ninety minutes each! If you want to have a maths competition (and I’m still not sure that we should!), in terms of preparing people for research careers, it would be a more realistic experience to make it a team competition, and to give people all day to work together on the problems to produce a single collaborative solution.

But why make it a competition at all? The Polymath project showed the value of “many eyes” on research problems, so if you are getting 500 of the smartest teenage mathematicians in the world together, then why not let them loose on the frontiers of maths, and get them to work on genuinely unsolved problems? There aren’t many subjects where this is even vaguely feasible, and not all areas of maths would qualify, but wouldn’t it be inspiring to see international collaborations forming in this way and genuinely advancing human knowledge?

So of course I feel privileged to have been selected for this team, and am grateful for the experiences that I had as a result. But any young mathematician who didn’t make the team certainly shouldn’t feel disheartened, because they’ve still got many chances ahead to contribute to the subject.