The dream of every aspiring young mathematician is to compete at the annual International Mathematical Olympiad (IMO), where the best pre-university maths minds from around the world are faced with subtle, challenging and imaginative problems.

As a competition it is brutal and intense.

I speak from experience; I was in the UK team in 2011.

So it was with great expectation that I went to see X+Y, a star-studded British film about the travails of a British IMO hopeful who is struggling against the challenges of romance, Asperger’s and really tough maths.

Obviously, there were a few oversimplifications and departures from reality necessary for a coherent storyline. There were other problems too, but we’ll get to them later.

In order to get chosen for the UK IMO team, you must sit the first round test of the British Mathematical Olympiad (BMO1). About 1200 candidates take this test around the country.

I sat BMO1 on a cold December day at my sixth form, Netherthorpe School in Chesterfield. Apart from the invigilator and me, the room was completely empty, although the surroundings became irrelevant as soon as I was captivated by the problems. The test comprises six questions over the course of three and a half hours. As is the case with all Olympiad problems, there are often many distinct ways to solve them, and correct complete solutions are maximally rewarded irrespective of the elegance or complexity of the proof.

Here’s a typical BMO1 problem (from 2006):

Find four prime numbers less than 100 which divide 332 – 232.

There are many ways to solve this, including using Fermat’s Little Theorem, modular arithmetic, and factorising the polynomial p32 – q32. A less efficient approach was taken by one student who attempted to manually evaluate 332 – 232 and perform a brute-force search of all primes below 100. It is difficult to imagine a more cumbersome method, short of using Roman numerals!

The knowledge required to solve this problem does not transcend A-level, but it demands thinking more laterally than is required in any conventional exam.

A few weeks later this is followed by a second and more challenging round, the BMO2, which consists of four considerably more difficult problems. Here’s a typical BMO2 question taken from last year:

We say that two integer points (a, b) and (c, d) in the plane can ‘see’ each other if the line segment joining them passes through no other integer points. A ‘loop’ is an irreducible non-empty set of integer points such that each element can see precisely two other elements of the set. Does there exist a loop of size 100?

The solution is quite involved and generalises to any bipartite graph. The idea is to put alternate vertices on the x- and y-axes, and to appeal to the Chinese Remainder Theorem in addition to Dirichlet’s Theorem in order to guarantee that this can be done in such a way as to ensure that the only lines of visibility are those that we specifically want.

The highest twenty scorers are invited to another training camp at Trinity College, Cambridge, and the top six are selected to represent the UK at an annual competition in Romania.

I was chosen for this. It was my first experience of an international maths competition, and indeed my first time abroad. Upon arriving at Luton airport, I was confronted with a scene of people wielding Rubik’s cubes and playing word games, not completely dissimilar from the airport scene in X+Y. The main difference was that my compatriots were far more friendly and agreeable than their arrogant and pretentious film counterparts. Instead, we had an immediate mutual respect.

Facebook Twitter Pinterest The British IMO team (together with the team leader and two other helpers) in 2011. Adam, then aged 17, is fifth on the left. Photograph: Joseph Myers.

In Romania, there was much maths, but we also enjoyed a snowball fight against the Italian delegation and sampled the delights of Romanian rum-endowed chocolate. Since I was teetotal at this point in time, the rum content was sufficient to alter my perception in such a way that I decided to attack a problem using Cartesian coordinates (considered by many to be barbaric and masochistic). Luckily my recklessness paid off, enabling me to scrape a much-coveted gold medal by the narrowest of margins.

In X+Y, the British team has a joint training camp with the Chinese delegation. The closest analogue is the Anglo-Hungarian training camp that is held near a picturesque but secluded lake thirty miles west of Budapest. From my experience in December 2011, this was the most enjoyable of the maths camps.

The connection between the UK and Eastern Europe is rather complicated to explain, being intimately entangled with the history of the IMO. The inaugural Olympiad was held in Romania in 1959, with the competition being only open to countries under the Soviet bloc. A Hungarian mathematician, Béla Bollobás, competed in the first three Olympiads, seizing a perfect score on the third. After his PhD, Bollobás moved to Trinity College, Cambridge, to continue his research, where he fertilised Cambridge with his contributions in probabilistic and extremal combinatorics (becoming a Fellow of the Royal Society in the process). Consequently, there is a close relationship between Hungarian and Cantabrigian mathematics.

Nathan (the protagonist of X+Y) receives a seated ovation when he presents a solution immediately after being asked a question involving playing cards by their team leader:

Can you also solve this question in the time it takes to say it?

This was highly unrealistic, as the question is entirely trivial in comparison with problems encountered at international level. That Nathan and I both solved it in a split-second is indicative of this – IMO-level problems typically take many minutes or even hours to solve.



In the film, the IMO is held at Cambridge. In 2011 it was in Amsterdam. I was impressed that the film managed to accurately capture the atmosphere of the exam, even in the detail of having exactly the same colour-coded cards for requesting assistance. Conversely, the overgrown lollipops bearing the mantra ‘Can I Help?’ were much less believable!

Rafe Spall’s character was very convincing, and his eccentricities injected some much-needed humour into the film. Similarly, Asa Butterfield’s portrayal of a “typical mathmo” was realistic. On the other hand, certain characters such as Richard (the team leader) were unnatural and exaggerated. In particular, I was disappointed that all of the competitors were portrayed as being borderline-autistic, when in reality there is a much more diverse mixture of individuals.

X+Y is also a love story, and one based on a true story covered in Morgan Matthews’ earlier work, the documentary Beautiful Young Minds. This followed the 2006 IMO, in China, where one of the members of the UK team fell in love and married the receptionist of the hotel the team were staying at. They have since separated, although his enamourment with China persisted – he switched from studying Mathematics to Chinese Studies.

It is common for relationships to develop during maths Olympiads. Indeed after a member of our team enjoyed a ménage-a-trois at an IMO in the 1980s, the committee increased the security and prohibited boys and girls from entering each others’ rooms.

I did not find the love story in X+Y convincing. But what was even more absurd was that a climactic moment was illustrated by a majestic, CGI rainbow that was optically inconsistent! The colours appeared in the same order in the inner and outer rainbows, which does not reflect (no pun intended!) actual double rainbows, where the colours appear in reversed order.

What happens to IMO veterans? More than half of UK team members since we joined the competition in 1966 have become (like me) undergraduates at Trinity College, Cambridge.

Facebook Twitter Pinterest Isaac Newton said that if he saw further it was by standing on the shoulder of giants. Here his statue stands at Trinity, by the shoulder of Adam P Goucher.

Trinity is something of a mathematical paradise, being the ancestral home of Isaac Newton, G.H Hardy, Srinivasa Ramanujan and many others. The community of Trinity undergraduates also help the effort by giving maths camp lectures, marking selection tests and (most importantly!) making tea. I myself assisted in founding the European Girls’ Mathematical Olympiad, which is now in its fourth year, and actively mark the corresponding UK selection paper.

Even though it wasn’t a faithful representation of Olympiad life, I hope that ‘X+Y’ inspires and encourages aspiring young mathematicians to pursue their interest to the highest level possible.

Adam P. Goucher is in the third year of a maths degree at Cambridge. You can follow his blog at Complex Projective 4-Space.



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