Tag Archives: coordination

IMO 2016 Diary – Part Four

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A pdf of this report is also available here.

Thursday 14th July

I have now spent a while thinking about square-free n in Q3 after rescaling, and I still don’t know what the markscheme should award it. I therefore request that Joe and Warren receive the same score as each other, and any other contestant who has treated this case. In my opinion this score should be at most one, mainly as a consolation, but potentially zero. However, we are offered two, and after they assure me this is consistent, I accept.

There is brief but high drama (by the standards of maths competitions) when we meet Angelo the Australian leader, who confirms that he has just accepted one mark for almost the same thing by his student Johnny. A Polish contestant in a similar situation remains pending, so we all return for a further meeting. I’m unconvinced that many of the coordinators have read all the scripts in question, but they settle on two for everyone, which is consistent if generous. The only drama on Q5 is the ferocious storm that sets in while I’m making final notes in the plaza. Again though, coordinator Gabriele has exactly the same opinion on our work as Geoff and I, apart from offering an additional mark for Lawrence’s now slightly damp partial solution.

And so we are finished well before lunch, with a total UK score of 165 looking very promising indeed. I’m particularly pleased with the attention to detail – Jacob’s 6 on Q4 is the only mark ‘dropped’, which is brilliant, especially since it hasn’t come at the expense of the students’ usual styles. We’ll have to wait until later to see just how well we have done.

It would be nice to meet the students to congratulate them in person, but they are with Jill on the somewhat inaccessible Victoria Peak, so instead I take a brief hike along the trail down the centre of HK Island, ending up at the zoo. This turned out to be free and excellent, though I couldn’t find the promised jaguar. There was, however, a fantastic aviary, especially the striking flock of scarlet ibis. A noisy group of schoolchildren are surrounding the primates, and one lemur with an evil glint in his eye swings over and languidly starts an activity which elicits a yelp from the rather harried teacher, who now has some considerable explaining to do.

With 1000 people all returning to UST at roughly 6.30, dinner is not dissimilar to feeding time at the zoo, and afterwards various leaders lock horns during the final jury meeting. Two countries have brought an unresolved coordination dispute to the final meeting, and for the first time since I became deputy leader, one of them is successful. Congratulations to the Koreans, who now have a third student with a highly impressive perfect score. Andy Loo and Geoff chair the meeting stylishly and tightly, and although there are many technical things to discuss, it doesn’t drag for too long. Eventually it’s time to decide the medal boundaries, and the snazzy electronic voting system makes this work very smoothly. I feel the gold and bronze cutoffs at 29 and 16 are objectively correct, and the 50-50 flexibility at silver swings towards generosity at 22. We can now confirm the UK scores as:

UKscoresThis is pretty much the best UK result in the modern era, placing 7th and with a medal tally tying with the famous food-poisoning-and-impossible-geometry IMO 1996 in India. But obviously this is a human story rather than just a 6×6 matrix with some summary statistics, and Harvey in particular is probably looking at the world and thinking it isn’t fair, while Warren’s gold is the ideal end to his four years at the IMO, two of which have ended one mark short. The American team are pretty keen to let everyone know that they’ve placed first for the second year in succession, and their remarkable six golds will hopefully allow scope for some good headlines. There is much to talk about, celebrate and commiserate, and this continues late into the night.

Friday 15th July

Our morning copy of the IMO Newsletter includes an interview with Joe, with the headline ‘Meh’. Frank Morgan has rather more to say, which is good news, since he’s delivering the IMO lecture on Pentagonal Tilings. He discusses the motivation of regular tilings where the ratio Perimeter/Area is minimised, starting from questions about honeycombs raised by the Roman author Varro! We move onto more mathematical avenues, including the interesting result of L’Huilier that given a valid set of angles, the associated polygon with minimal Perimeter/Area has an incircle, and the corresponding result for in-n-spheres in higher dimension. A brief diversion to the beach on the way home is punctuated with attempts to project the hyperbolic plane onto the sand.

The day’s main event is the closing ceremony, held at the striking Hong Kong Convention Centre. As usual, the adults and our students have been vigorously separated for the journey. As I arrive, it seems the UK boys have been directing a massed gathering behind the EU flag on stage, while the non-European teams are divided into two sides in a giant paper aeroplane dogfight. All attempts by the organisers to quash this jocularity are being ignored, and after bringing everyone here two hours early, I have minimal sympathy. Geoff sits on a secluded bench, and agrees to the many selfie requests from various teams with regal if resigned tolerance.

The ceremony is started by a fantastically charismatic school brass band, and proceeds with some brief speeches, and more astonishing drumming. Then it’s time to award the medals. Lawrence and Jacob get to go up together among the clump of 24-scorers, while Kevin from Australia does an excellent job of untangling his flag and medal while keeping hold of the ubiquitous cuddly koala. Neel has been threatened with death if he appears on stage again with an untucked shirt, but no direction is required for his and Warren’s smiles as they receive the gold medallists’ applause.

P1010513 (3)Afterwards, there is a closing banquet. We get to join British coordinators James and Joseph for a climate-defying carrot soup, followed by a rare diversion onto Western carbohydrates accompanying what is, for many of us, a first taste of caviar. Both Geoff and the American team are forced to make speeches at no notice. It is all generally rather formal, and fewer photographs are taken than usual. An attempt to capture Joe and Harvey looking miserable results in one the biggest grins of the evening. The UK and Australian teams have a thousand stickers and micro-koalas to give out as gifts, and some of the attempts at this descend into silliness. All clothing and body parts are fair game, and Jacob makes sure that Geoff is fully included. The UK and Australian leaders, variously coated, retreat from the carnage to the relative safety of our top-floor balcony as the IMO drifts to an end, until midnight, when it seems sensible to find out what the students are up to.

Saturday 16th July

This is what the students are up to. When we arrived at UST last week, everyone was given food vouchers to redeem at the campus’s various restaurants. Very very many of these are left over, and, despite the haute cuisine on offer earlier, people are hungry. They have therefore bought McDonalds. And I mean this literally. Animated by Jacob and American Michael, they have bought the entire stock of the nearest branch. If you want to know what 240 chicken nuggets looks like, come to common room IX.1, because now is your chance. Fortunately our team have made many friends and so after the Herculean task (I make no comment on which Herculean labour I feel this most resembles) of getting it to their common room, pretty much the entire IMO descends to help. Someone sets up a stopmotion of the slow erosion of the mountain of fries, while the usual card games start, and a group around a whiteboard tries to come up with the least natural valid construction for n=9 on Q2. Around 3.30am everything is gone, even the 30 Hello Kitties that came with the Happy Meals, and we’re pre-emptively well on the way to beating jetlag.

I wake up in time to wave Geoff off, but he’s been bumped to an earlier bus, so the only thing I see is Lawrence and colleagues returning from a suicidal 1500m round the seaside athletics track. Our own departure is mid-morning, and on the coach the contestants are discussing some problems they’ve composed during the trip. They’ll soon be able to submit these, and by the sounds of it, anyone taking BMO and beyond in 2018 has plenty to look forward to. Jacob has already mislaid his room key and phone, and at the airport he’s completed the hat-trick by losing one of the two essential passport insert pages. Fortunately, it turns out that he’s lost the less essential one, so we can clear security and turn thoughts towards lunch.

Jill has given me free licence to choose our dim sum, so the trip ends with pork knuckle and chicken feet. Our aim is to stay awake for the whole flight, and Neel helps by offering round copies of a Romanian contest from 2010, while I start proof-reading. By the time they finish their paper, many rogue commas have been mercilessly expunged. It should be daylight outside, but the windows are all shut, and by the ninth hour time starts to hang drowsily in a way that combinatorial geometry cannot fix, and so the mutual-waking-up pact kicks in, aided by Cathay Pacific’s unlimited Toblerone. Winding through Heathrow immigration, Joe unveils his latest airport trick of sleeping against vertical surfaces. We diverge into the non-humid night.

Reflection

IMG_0468 original (2)There’s a great deal more to life and mathematics than problem-solving competitions, but our contestants and many other people have worked hard to prepare for IMO 2016 over the past months (and years). So I hope I’m allowed to say that I’m really pleased for and proud of our UK team for doing so well! The last three days of an IMO are very busy and I haven’t had as much time as I’d have liked to talk in detail about the problems. But I personally really liked them, and thought the team showed great taste in choosing this as the British annus mirabilis in which to produce lots of beautiful solutions.

But overall, this is really just the icing on the cake of a training progamme that’s introduced lots of smart young people to each other, and to the pleasures of problem-solving, as well as plenty of interesting general mathematics. I have my own questions to address, and (unless I’m dramatically missing something) these can’t be completed in 4.5 hours, but as ever I’ve found the atmosphere of problem discussion totally infectious, so I hope we are doing something right.

Lawrence and Warren are now off to university. I’m sure they’ll thrive in every way at this next stage, and hopefully might enjoy the chance to contribute their energy and expertise to future generations of olympiad students. The other four remain eligible for IMO 2017 in Brazil, and while they will doubtless have high personal ambitions, I’m sure they’ll also relish the position as ideal role models for their younger colleagues over the year ahead. My own life will be rather different for the next two years, but our camp for new students is held in my no-longer-home-town Oxford in a few weeks’ time, and I’m certainly feeling excited about finding some new problems and doing as much as possible of the cycle all over again!

IMO 2016 Diary – Part Three

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Sunday 10th July

I’m awake at 6am and there’s nothing to do, so take a short run along the edge of the bay. I meet an old lady singing along to a walkman (yes, really) while doing taichi. She encourages me to join and it seems rude to refuse. Suffice it to say I’m as grateful no video evidence exists as she should be that no audio recording was made. Six-hundred mathematicians queueing for powdered eggs seems like an unwelcome start to the day, so we are self-catering. The guides have been commanded to show every student how to find their place in the exam hall, and I approve of Allison’s contempt for the triviality of this task.

The main event of the day is the opening ceremony, held at the Queen Elizabeth stadium in the centre of Hong Kong Island. To no-one’s surprise, this involves a lot of time waiting around in the stifling UST plaza, which the students use to take a large number of photographs. The UK and Australian boys are smartly turned out as usual, but the polyester blazers are rather ill-suited to this tropical conditions, so we invoke Red Sea rig until air conditioning becomes available. The Iceland team are particularly keen to seek out the English members for reasons connected to a football match of which Neel proudly claims total ignorance. I picked up an EU flag for next-to-nothing last Friday, and now Jacob and Warren prove very popular as they circulate inviting our (for now) European colleagues to join us behind the stars.

The deputies are segregated in an upper tier and obliged to watch a rehearsal of the parade. Some of the organisers have a confused interpretation of the IMO roles. I still have some of the uniform with me, but an official says it is literally impossible for me to give it to the team. She is small and Joe Benton can catch flying ties as well as colds, so it turns out to be literally entirely possible, but for my trouble I get called ‘a very bad boy’.

Many hours after we left our rooms, the ceremony starts, and is actually very good, with a handful of well-chosen speeches, a mercifully quickfire parade of teams, and musical interludes from a full symphony orchestra, with various traditional and non-traditional percussion. The new IMO song Every day in love we are one involves a B section accompanied by a melange of watercooler bottles, but despite its catchy conclusion about maths, friendship and beyond, I suspect it may not trouble the top of the charts.

Monday 11th July

It’s the morning of the first IMO paper, and you can feel both the excitement and the humidity in the air. Some of our boys are looking a bit under the weather, but we know from past experience that the adrenaline from settling down in a room of 600 young contestants who’ve been preparing for exactly this can carry them through anything. I skip an excursion in order to receive a copy of the contest paper. Security is tight, and the deputies who have chosen this option are locked in a lecture theatre for two hours, and our bathroom visits monitored with commendable attention to detail. I guess that the combinatorial second problem is most likely to provoke immediate discussion, so I spend my time working through the details of the argument, just in time to meet our contestants when their 4.5 hours are up.

Q3 has been found hard by everyone, and Q2 has been found hard by other countries. Harvey’s kicking himself for drawing the wrong diagram for the geometry, an error that is unlikely to improve Geoff’s mood when he receives the scripts later today. Apart from that, we have a solid clutch of five solutions to each of the first two problems, and various nuggets of progress on the final problem, which is an excellent start. Several of the team are itching to keep trying to finish Q3, but the campus is likely to be annoying hotbed of spurious gossip all day, so Allison and I take them out. The very convenient MTR takes us under the harbour while the students and I debate the usefulness of the square-free case, and how well it is preserved under rescaling so that the circumcentre is a lattice point.

As we emerge above ground, Jacob is entranced by the live-action Finding Dory playground at Causeway Bay, and we toy with buying a pig’s trotter from a nearby market, but not even Lawrence is feeling adventurous enough with another exam tomorrow. We travel over to Kowloon via double-decker tram and ferry, and fortified by ice cream, take lots of photographs of the unique HK skyline, where even the giant waterfront office towers are dwarfed by Victoria Peak, which the contestants will visit while I’m marking. On our return journey, some of the team are impressed by the HK rush hour, indicating that they’ve clearly never tried to change line at Leicester Square around 6pm on a Friday…

Tuesday 12th July

Another morning, another trek uphill to a 4.5 hour exam. Time passes rapidly, especially now I’ve worked out how to order coffee without the ubiquitous condensed milk. The security arrangements concerning the deputies’ copies of the paper have been increased even further, but the IMO photographers have outdone themselves, and published on Instagram some pictures of the exam room with a level of crispness such that it’s clear the paper includes no geometry, and after finally getting hold of a proper hard copy, it looks like a paper which the UK team should really enjoy.

As so often after IMO papers, there is a range of reactions. Lawrence is unsure whether he presented his exemplar polynomial in a form that actually works. Joe knows and I know that he could easily have got at least 35 on these papers, but after over-meta-thinking himself on Q5, this isn’t his year. Like Aeneas gazing on the ruins of Troy, sunt lacrimae rerum, but also plans for new foundations. By contrast, Harvey has atoned for yesterday’s geometric lapse with what sounds like a perfect score today. Warren and Neel seem to be flying overall, and are doing a good job of keeping their excitement under control while the others muse. There’s plenty to think about, and Geoff has now arrived bearing yesterday’s scripts and several novels’ worth of anecdotes from the leaders’ site.

Before getting down to business, it feels sensible to walk off the Weltschmerz, and provide an outlet for joy in the nearby Clearwater Bay country park. There’s a long trail all over the New Territories, and we join it for a brief but purposeful stroll up through the light jungle and along the ridge. We’re confident we didn’t find the global maximum, but we find a couple of local maxima with great views out around the coastline, which seems to have Hausdorff dimension slightly greater than 1. We see some enormous spiders (though the Australians are substantially less impressed) before ending up an uncontroversial minimum where Jill has bedded in with merciful bottles of water on the beach. To say we are sticky doesn’t even begin to cover it but, crucially, we are no longer consumed by the morning’s events.

The UK boys are now masters of the complicated UST food court ordering process, and Warren endears himself to Geoff by producing a steaming bowl of spicy ramen as if by magic. The contestants have a ‘cultural night’, which apparently includes a greater number of hedge fund representatives than one might have expected. For me, it’s a night in with Geoff, green tea and the scripts for Q2. Joe and Neel have filled fourteen pages between them checking a construction in glorious detail, a step which Harvey has described in its entirety with the words ‘glue them together’. Overall, they are complicated but precise, and I have few concerns, so it’s only necessary to burn the candle at one end.

Wednesday 13th July

It’s time for coordination, where Geoff and I agree the UK marks with a team of local and international experts. The scheduling has assigned us the Q1 geometry early in the morning, which is a clear case of five perfect solutions, so we move to Q2. Coordinator Stephan seems very well-prepared for the UK scripts, so again we are finished in a matter of minutes. This allows us to bring forward our discussion of Q4. Jacob has made several small errors, all of which could be fixed by attacking his script with a pair of scissors and some glue. I believe the mark scheme should award this 4+2, and coordinator Juan thinks it should be 5+1. We are both open to each other’s interpretations, and have at least basic proficiency in addition, so again there is little need for debate.

The early evening brings the main challenge of the day, Q6, at which the UK has excelled. Our frogmaster Geoff has listed marks for five of our attempts, but the final script belonging to Joe has generated only the comment ‘magical mystery tour’. His solution to part a) diverges substantially from the most natural argument, and indeed involves wandering round the configuration, iteratively redirecting lines [1]. I am eventually convinced by the skeleton of the argument, though unconvinced I could complete the details in the finite time available.

We discuss the script with Lisa Sauermann, who explains some of the main challenges [2]. After a short pause for thought, we’re convinced by Lisa’s suggestion of equivalence with a point on the conventional markscheme. It would have been nice to have had more time to think about the subtleties myself, but this was some really interesting maths and we pack up for the day feeling very impressed with the quality of coordination here so far.

We and the coordinators are also very impressed with the quality of Harvey’s art. As a result, we now have an answer to the question ‘What should you do if you finish the IMO two hours early?’ Harvey’s answer at least is to draw a diagram of the Q6 configuration in the case n=3, where at each of the intersection points with the outer boundary stands a member of the current UK team. Precisely UNKs 1, 3 and 5 are wearing a frog. The real life sextet have been taken by Allison to Disneyland today, so some are potentially now wearing a princess. But while the contestants can let it go now, it’s off to work I go, as there’s still two sets of scripts left to ponder.

Harvey Q6[1] The mechanism for this redirection is neither canonical nor explained, and even in the best setup I can come up with in an hour or so of trying a huge class of diagrams, exactly half of the indices in the resulting calculation are off by \pm 1. The pressure of IMO Day Two can indeed derail even the most well-prepared contestants.

[2] There is a non-trivial difficulty when the area enclosed by our path is concave, as then some intersection points on the path arise from lines which are also part of the path. Handling the parity of such points looks easy once you’ve been shown it, but is definitely not obvious.

IMO 2015 Diary – Part Four

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Sunday 12th July

I spend many hours reading the students’ scripts for the medium questions 2 and 5. Psychologically, this solitude is quite a sudden shift after so many days of constant group interaction. Although only one of the twelve solutions is complete, I’m really pleased with how everyone has presented their progress. We’ve spoken a lot at the camps during the year about how to write up maths under various kinds of pressure so that it is intelligible to other human beings. All the boys have been very clear this year, so they should get plenty of marks and coordinating won’t cause much drama.

By comparison with the student site, the leaders’ hotel has slightly better views, slightly better food, and an even more appalling lift availability algorithm. When the work is done for the day, I meet Jill and the students at the night market, where Lawrence is sharing round a packet of fried giant crickets. They have enjoyed their excursion, especially the visit to an umbrella and other handicraft factory, where it seems they did their best to re-inflate the Thai economy. Neel has a three foot wide fan, hand-painted in a style evoking My Little Pony. While it doesn’t quite conjure the demure grace of, say, Callas as Madam Butterfly, it does induce a billowing wind tunnel effect, which is appreciated in the back of our taxi.

Monday 13th July

Today is the main day of coordination, when Geoff and I meet local markers to agree the UK students’ scores. Over breakfast we decide to ask for a solitary 1 for Joe’s hastily-written summary of Q6 in our first meeting. After some not especially thrilling wrangling about the meaning of the phrases ‘combinatorial description’ and ‘non-trivial progress’, we get what we want without having to deploy my carefully-worded speech.

This will turn out to be by some margin the most challenging meeting. On Q2, they have already decided to forgive Warren’s microscopic omission, and the mark schemes are extremely precise, especially for the middle problems which normally cause the most trouble. Everyone seems to be interpreting them sensibly and similarly so there are no delays, and we are able to bring forward the easier geometry meeting, and confirm all our marks by 5pm. We have {10,17,19,19,19,25}, which is certainly respectable, even if it does mean, to Geoff’s infinite chagrin after his boasts at breakfast, that we are beaten by France.

We’ve been keeping the students up to date via text while they’ve been petting elephants and dipping their feet in hot springs. We meet them for dinner, where they are disappointed at the lack of dramatic gossip about the process, but pleased with their scores, especially the efficient accumulation of part marks on the harder questions. It remains to be seen tomorrow what colour of medals all of this will generate.

Tuesday 14th July

While the UK is done, and I find some more obscure temples in town, other countries continue their final coordinations. It looks like Australia will have its best ever performance, with at least two students sure to receive gold medals, and the rumour is snowballing that USA has won, for the first time since the mid 90s. The students have been attending the IMO lectures this morning, and it seems that Ravi Vakil’s talk on `The Mathematics of Doodling’ has really got the UK boys thinking about space and the meaning of orientation.

Tiring of the comical lift process, I investigate the hotel’s external fire exit, disturbing a flock of pigeons, and a rat the size of a small dachshund. In pursuit of more interesting wildlife, Jill suggests we take the students to Chiang Mai Zoo for the afternoon. Sam and Harvey enjoy the real-life version of Hungry Hippos, and we find an enclosure with a large (ie at least 9), odd number of tortoises, of which precisely one is feeling rather, ahem, left out. The main attraction though is the giant panda Chaung Chaung, who we get to see eating his bamboo with the satisfied langour of a chubby toddler.

We diverge again so I can attend the final jury meeting, where after some brief admin, we pass rapidly to the medal boundaries. There is a new protocol in place this year, which I will leave for Geoff to explain, but the only non-trivial decision to be made is whether the gold cut-off should be rather higher than ideal or slightly lower than ideal. I disagree very strongly with some of the baffling comments which are made on both sides, but only the leaders have a say in this, and the end result is a narrow victory for the higher cutoff*. The UK upshot is that our triumvirate scoring 19 scrape into the silvers, while Warren unfortunately misses out on gold by one point for the third competition in a row. It’s hard to know what to say in these circumstances, but at least by meeting up with the Australian and American teams, we find other students in similar positions, and the feelings of elation and disappointment can be more widely shared.

[*As a result, about 1/15 rather than the statuted 1/12 students get the top award. The other option would have been 1/10.5. So all those leaders concerned about the ‘de-evaluation of the gold’ etc can sleep easy. So can any of their current and past gold-winning students, who had been so worried about retrospective reappraisal of their abilities. You’re right – this was ludicrous.]

Wednesday 15th July

I’ve got the rest of my life to lie in, so decide to cycle to the temple at the top of Doi Suthep. I rent the fanciest bike I can find, for B300, and, to the astonishment of everyone, a helmet for B200. Given the standard of driving, which is at times even worse than Colombia, this seems an absolute bargain. The ride itself though is more exertive than enjoyable, with no real views except the temple at the top, which is more extensive and more gold than the others in town, but also far more busy, which rather spoils the effect.

The real business of the day is the closing ceremony, held through the afternoon in the giant theatre within the student hotel. There’s an excellent drumming and dancing ensemble, and a beautifully-edited video of the IMO activities, which one probably ought to describe as comprehensive rather than a vignette. After about an hour, the medals are awarded, with a great deal more efficiency than normal. The idea to go in decreasing order of score within increasing order of medal is unusual, but does mean that our 19-ers receive their silvers together. Warren and Michael from USA compete for who can get their flag in the premier position. There are a few speeches, and a preview of IMO 2016 in Hong Kong, before we are released for more photographs and an early dinner.

The notion of having an indoor food market as part of the closing banquet is a good one, though it is a struggle to decide whether items are sweet or savoury. Lawrence, Joe and Sam get the chance to show off just how far their chopstick abilities have improved with tricky numbers like ribs and fruit salad. Then the live music starts, and whoever did the soundcheck has some questions to answer, as we can genuinely feel the bass vibrating through our chairs. We retire to the lobby which is, despite the continuing efforts of Elvis, much quieter. As various teams gather, and the students loiter to make final use of the games in the recreation room, this year’s IMO draws to a close.

Thursday 16th July

My flight to Mandalay is not until later, but I join Geoff to meet the rest of the UK group at Chiang Mai airport at 7am. Some of our students are looking rather rough round the edges, for a mixture of illness- and fatigue-related reasons, and there is enthusiasm only for a final round of anti-nausea medication. I’m sure it will be a fun 36 hours for everyone. In any case, soon they are off for a 12 hour layover in KL then home, and I have several hours to ponder.

My only negative thought about this year’s IMO was that the difficulty of the papers reduced the number of students who could feel the satisfaction of completing a medium or hard problem. Earning silver medals based on the easiest problems and part marks is not, in my opinion, entirely the idea, but of course it is the same for everyone. It’s probably also a good reflection on our training programme that the majority of our students feel they wanted to do much better, while we nonetheless came 22nd, with an entirely respectable medal haul. Certainly any disappointment felt about this result should not negate the value of everything they’ve learned by solving problems, and from discussions with each other and the staff during our training. In all other regards this IMO seemed a triumph. Students from all countries seem to have enjoyed themselves, and I’ve had a good time too.

Our camp for new students will be held in Oxford in just a few weeks’ time, and five of this team are eligible for Hong Kong next year. There’s plenty of interesting mathematics just around the corner. But right now, I’ve got to board the world’s most questionable aircraft, so consider it announced that I might have solved the Riemann hypothesis, and we’ll let fate run its course.

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Final Words

Training a UK team and taking them to the IMO requires a huge amount of effort from a large number of people. Thanks are particularly due to:

  • All the academic and pastoral staff at our camps this year in Oxford, Hungary, Cambridge and Tonbridge, and the UKMT office, especially Bev, who ensured everything ran smoothly. Also everyone who helped set just about enough problems to sate the voracious appetites of our students.
  • Alison, Lina, Mun, and the other staff at Nexus International School, where our stay was pleasant and conducive to good mathematics.
  • Everyone involved with IMO 2015 who ran a competition which was, from the angles I saw at least, almost faultless. In particular, our guide, Korn, who couldn’t have been more helpful. We all wish him the best as he moves to Columbia next month.
  • Paul Janssen, the inventor of Imodium, without whose contribution to science many moments of this trip would have been much less comfortable for the protagonists.
  • Geoff and Jill, who were excellent colleagues in every sense through the challenging and the joyous moments of this year’s trip.
  • Our team, comprising Joe, Lawrence, Sam, Warren, Neel and Harvey, who are all thoroughly nice people. It’s been a pleasure to watch them improve together through the past few months, and I’m sure they will go far in whatever mathematical or non-mathematical avenues they choose over the years to come.

IMO 2014 – Part Four – Coordination and Close

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Thursday 10th July

At last year’s IMO, a discussion arose concerning which of the seven members of the UK delegation at lunch was most likely to be the deputy leader. I placed rather low down the list. Despite the fresh-faced nature of the 2014 team, I’m taking no chances this year and now have a fairly full beard. However, today we have the first of our meetings with the coordinators to agree the UK team’s marks, and it may be necessary for Geoff and I to play good cop/bad cop. I prefer to play bad cop and feel this is a role best approached clean-shaven. In any case, there is a clash of timings so after signing for a vector of zeros on Q6, I end up playing solo cop on Q2.

We start with Frank, who has tried to prove something more general in one place, which is unfortunately false, but would be true in the special case. He then uses this in the second part of the problem, referencing the false bit, but using only the bit which is actually true. His habit of putting bold circles round sections he thinks are dubious is heart-warmingly honest, but I wonder whether it might have made more sense to use the time at the end of the exam to un-dubify them, rather than operating a series of nested post scripts? In any case, rather by an accident of the markscheme, we are offered 4, which is what I was hoping for, but definitely more than I was expecting. We also agree a 7 on Warren’s solution, and after coordinator Robert dramatically waves a diagram of a common counterexample to Harvey’s final argument at me, we agree a 5 for him.

The others are more tricky. Joe has done both parts of the problem fundamentally correctly, but has written down the final answer incorrectly. Since this step is genuinely trivial, it seems harsh to dock it a mark. Especially since the coordinators didn’t notice until we pointed it out to them. Hopefully this should be squashed overnight, though ultimately it is likely that several students will have done this, so consistency is all one can ask for. In any case, I regret my cavalier assurance straight after the exam. Freddie is offered 7, but also has a tiny mistake that they have not noticed. In fairness to them, this is very hard to spot, with the construction of an extra point in an extremal argument failing only in the case (2,2) out of [1,n]\times [1,n], but they insist it has to be a 6. Coordinator Santiago reminds me that a proof is not a proof if it contains a mistake. This is a true statement. We will reconvene tomorrow.

The team have got back from their own excursion to Cape Point and seem to have enjoyed themselves, even the extended musical lunch. It would be nice to be able to give them more information about their marks, but they will have to bide their time. Perhaps in preparation for IMO 2015 in Chiang Mai, we return for a fifth visit to the Thai Cafe in Rondenbosch where both sides give a fuller exposition of their activities during the day. Afterwards, I see the team appropriating one of the giant Google cubes that have appeared round the site. They reassure me that they are still taking the medication for kleptomania, and in fact they intend to use it to distribute the UKMT playing cards as gifts to the other contestants.

Friday 11th July

Again I spend much of the night wading through slicks of combinatorial vomit, now including Q5, perhaps ambitiously described as Number Theory. After Geoff gets exactly what we want on Q1 and Q4, I’m raring to go for an early fourth session on Q2. The French leaders have a student in a similar position to Joe and have threatened to take his case to the jury. They get the extra mark, and in the spirit of Agincourt and Trafalgar I’m only too happy to coast in on their wave. Gabriel, from whom there were plans to drop two separate marks for the same mistake, gets his 6, and after successfully countering yesterday’s counterexample, so does Harvey. Freddie’s appears to be still under discussion, and I find myself saying “With respect…” several times, before it transpires that actually they are trying to offer 7, which of course we take. While it’s easy to criticise, I should emphasise that this question a) was an absolute nightmare; b) had a harsh markscheme, but this was certainly consistently enforced; and c) ultimately if the students hadn’t made mistakes none of this would have been relevant. Our coordinators knew the scripts well, were reasonable and fair, and I can only imagine how difficult it must be to do it all over again in Uzbek.

Question 5 proceeds much more smoothly, starting with our observation that Warren’s script looks identical to the official solution, including the location of the page break. He and Harvey get 7s with no real debate, and after a brief examination of the Chinese characters in Frank’s rough it turns out we are in agreement on the other four marks too. This was a very well-constructed markscheme for part marks. It is sensible to be both generous and sub-additive and it felt like there was not much room for ambiguity, though I’m glad we didn’t have any almost-complete solutions.

We are finished rather earlier than expected, with a nice bunch of scores between 20 and 28, and a team score of 142 looking likely to place the UK in the high teens. This is a strong team performance. The ‘easy’ (of course, this is relative) questions 1 and 4 have been dispatched and we have scored well compared to other similar countries on the medium questions. This is what we train for, and it is excellent to see it bringing rewards. Our younger students will have more practice and experience and will earn more marks on the hard questions in years to come. In any case, Geoff and I are very pleased. I am thus able to join the team for a second, sunnier attempt at Table Mountain. I arrive in time to see the end of the team’s latest instalment of ‘play a round of bridge in unusual places’, and even get to see a group of dassies sunning themselves on the cliff edge. Some of the group are tired or nervous about medal boundaries, but the remainder head for a walk to Maclean’s Beacon, the highest point on the summit. It goes without saying that the views were beyond comparison.

After seeing the eland on Wednesday, I feel obliged to branch out and try one of their steaks, but in fact the kudu was marginally nicer. Marginals are up for grabs after dinner, as it’s time for the final jury meeting, featuring the confirmation of UK as host of IMO 2019, and the all-important medal boundaries. First there is discussion of various administrative matters, and thanking various people involved in the five official languages. There are long delays while the microphone is carried round the room. Geoff makes several speeches. For these the lack of microphone proves no problem. Eventually the flashy software brings up the crucial bar charts, and the boundaries are decided. A decision has to be made about whether to award medals to 47% or 53% of contestants. Either way, the boundaries are lower than I had expected, leaving us with 4 silvers and 2 bronzes. It is a shame for Frank and Freddie to miss out so narrowly, and perhaps a surprise for Warren that he ends up only one mark off a gold, but of course these things will happen, and it is no reason not to enjoy the festivities into the night.

Saturday 12th July

While the previous night featured slicks of mathematical vomit, last night offered a digression onto genuine vomit. No hard feelings Joe. We’re now even given that I hit him over the head with a punt paddle the first time we met. I have too many spotty socks anyway, and certainly couldn’t have dealt with another night of combinatorics. While he sleeps off whatever it is he’s caught, Jill and I get mildly stressed, and the team head off on an excursion to the Waterfront. Free entrance to the aquarium is by some margin the best feature, with a remarkable collection from both the oceans that converge on the Cape Peninsula. The team debate whether the Coriolis effect or some form of social self-reinforcement process is responsible for all the fish swimming clockwise, while they play yet another round of bridge (four clubs in case you were wondering) in front of the shark tank. Geoff makes the mistake of offering to wait for us while we obtain lunch, in a further demonstration that South Africa doesn’t really understand the first word in the term ‘fast food’, while Gabriel wants me to verify that a watch he’s planning to buy is genuine. I feel there do exist things which fall outside the deputy leader remit.

I’m definitely catching Joe’s affliction, so I sleep while the team get ready for the closing ceremony. By the time I wake up, the Google cube is already dressed in the Union Jack, filled with the fetching playing cards, and providing everyone with a good core workout as they manoeuvre it onto the bus. I enjoy what I see of the closing ceremony, in particular the excellent and strident youth choir. No mewling Anglican tenors on show here. A traditional ‘praise singer’ comes onstage and shouts about maths for about three minutes, which is less impressive, but equally entertaining. Our master of ceremonies returns, wearing the exact chromatic inverse of his outfit at the opening ceremony, and guides the medal presenters and recipients through their steps. Initially this is tricky, as there are substantially more bronze medal presenters than room on the stage.

The UK team are consummate professionals of course, managing the task (found tricky by many of their competitors) of getting the medal in front of the flag, and orienting the latter correctly. Harvey positions himself well so gets his medal presented by Geoff. Gabriel does not position himself well, so disrupts the linear ordering to get his medal presented by Geoff. Photos are taken in huge quantities. The team’s plan to distribute the cards to contestants as they leave the stage is to my astonishment a) working and b) not hugely annoying the organisers.

I make a brief run down the mountain to check on our sleeping silver medallist. On returning it seems the organisers are grateful for his absence, as they ran out following the unexpected boundaries, evinced by Warren’s prize, which does indeed appear to be a spray-painted bronze. I have missed Geoff being presented with a vuvuzela in recognition of his maximally numerous contributions to the jury. Like a toddler on Christmas morning, I suspect his new toy may ‘get broken’ at some point fairly soon. This is more of a reception than the usual sit-down affair, and the remainder of our team seem to be happily mingling, so there is time to say all the requisite goodbyes, and reflect on an excellent competition. Gabriel chooses 12.45am as the moment to ask US leader Po-Shen the question about probabilistic combinatorics he’s been brewing all week. Let it never be said that social convention stood in the way of good mathematics.

Sunday 13th July and Conclusion

I need to be in France, and Frank needs to be in North-East China, so we are leaving earlier than the rest of the group. Joe appears to be operational again, and receives his silver medal in front of a small but adoring crowd at breakfast. Muffins are again served with grated cheese, goodbyes are said, the final Rand are changed back, and we are off.

My journey to Paris via Dubai was highly unpleasant, and my view of the Emirates was mainly through the bottom of a paper bag, so I won’t dwell on that at all.

What I should dwell on is what an enjoyable year and an excellent IMO we’ve experienced together. I understand why peers and colleagues might well ask why I choose to come to the olympiad rather than take a conventional holiday, but this was a great event to be a part of, and a great group of people to travel with. I hope I’ve given a flavour of the students’ enthusiasm for problems in this report. It was entirely infectious, and we of course enjoyed all the other possibilities which two weeks in Cape Town offered us.

For me, there was a particularly pleasing cyclicity to lead a team at the IMO including Freddie and Gabriel, who were junior students at the first summer school I taught at, and though they are perhaps disappointed not to have made a bigger splash in the competition, they and Frank have been entirely excellent people to know over the past few years, proving exemplary models to their younger colleagues both mathematically and generally. We will miss them as students, but equally look forward to working with them as colleagues in the future, should they wish. While we missed the starry heights of 2013, this was nonetheless an excellent team performance, and with young team members, young reserves, and plenty of talented and keen students getting involved at all levels, the future seems bright for UK maths. I hope that our activities through the year to come will be as enriching for everyone as it has been in 2014.

IMO 2013 – Part Four: Co-ordination and Close

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Thursday 25th July

There is commotion at the adjacent (Netherlands?) table at breakfast when a large iguana steals a piece of bread then climbs onto a low-hanging branch to gloat over the spoils and relieve itself into their ceviche. Geoff and I also have some difficult encounters with the locals ahead today, as it is the first day of co-ordination.

This is the process by which the exam papers are marked. Geoff and I have looked at the UK students’ scripts, as have a team of local markers, called co-ordinators, who are split between the six questions. In an ideal world, all parties agree on the appropriate mark, so we can sign and head to the beach. In practice, however, the co-ordinators have very little reading time per solution, and are also responsible for ensuring the mark schemes are consistently applied.

Geoff has the 9am slot for Q4. Despite having prepared meticulous analysis of each UK student’s diagram dependency, we sign for 42/42 in a matter of seconds. Not such a baptism of fire after all. I am dealing with Q5 after lunch. They feel that Sahl has not finished the problem. I explain his argument in a slightly less minimalist fashion and they agree, getting the 41/42 we were looking for. We finish the day with Q1, which proves as straightforward as Q4.

Everyone is very pleased with progress so far, but also aware that tomorrow will be the tricky day, with the three hardest questions, including two which feature long combinatorial essays rather heavily. Geoff and I retire early to immerse ourselves in mathematics.

In the end I do spend a token amount of time asleep. Q6 is the main cause of my insomnia. Andrew has written a long argument that astonishingly combines both official solutions. Unfortunately he claims some results as trivial which the model answer devotes up to a page to proving, so we fear 6 is the best we can hope for, though explaining what is going on may take some time. Meanwhile Matei has come up with a very satisfying original argument, but has run out of time to finish it. In order to convince the co-ordinators that this will work, I cobble together the final steps and practice my speed-LaTeX while the sun rises.

Friday 26th July

First thing in the morning, and Geoff is trying to snare some partial marks on the hard geometry Q3. We feel Andrew deserves a point for some non-trivial progress in his rough work. The co-ordinators disagree and despite his entreaties we are forced to sign for a total of zero. The double combinatorics slog begins after lunch with Q2. We are able to get an extra mark for Gabriel bringing him to a total of 25 which will now surely be enough for a silver.

We are scheduled to be last to co-ordinate Q6, at 5.30pm. Aware that our arguments might take a while, and reluctant to hold up the machinations of the entire competition, we loiter and hope for an earlier slot. We end up with the problem captain for Q6 and the chief co-ordinator for all problems, so there would be no higher authority to resolve any disputes apart from an unprecedented (for the UK) appeal to the jury.

Daniel’s work turns out to be the main problem. He has not had much time, so has done the calculations for the increments of the inductive construction, and merely described how the induction itself works. The mark scheme looks very rigid, but appears to offer 4 marks for this, so I ask for that, and predictably the co-ordinators look surprised. We wrangle for a very long time indeed, but in the end I’m unable to convince them that despite the lack of proofs of the more technical part of the solution it is still worth at least 3. This extra mark would have earned Daniel a gold medal, so it is a shame, but he can perhaps draw some consolation from the fact that the regime was undoubtedly applied very fairly.

Matei and Andrew’s arguments also require lots of attention, and I am glad I prepared thoroughly, but in the end we get the 5 and 6 respectively that we wanted. They are now ensured strong gold medals. Geoff and I retire to the bar to toast what has been a record-breaking performance by the team, coming 9th overall, and top of the EU by some margin.

There follows the final jury meeting, where speeches are made by various team leaders, before the decision on the medal boundaries. There are no real controversies, and we end in good time to celebrate with our success and friends’ successes (not least a 15th place for Australia and top-ten individual score for AUS2 Alex Gunning) late into the night. I fear the supplies of Cachaca have been hit rather hard.

Saturday 27th July

The optional morning excursion to the nearby town of El Rodadero is generally spurned in favour of a lie-in and a final chance to enjoy the beach and the pool on the roof of my hotel. Since their well-deserved success may necessitate press releases and the like, the team are particularly encouraged to avoid obvious sunburn for the inevitable photos later.

The now-familiar convoy of buses gathers at dusk to transport the IMO to the nearby Quinta de San Pedro Alejandrino, site of Simon Bolivar’s impressive tomb, and location for the closing ceremony. First there are several speeches and performances from traditional singers and dancers. The mixing desk suffers some unfortunate problems, so the sound engineering for the ridiculously skilful young accordion player consists of a technician walking a single microphone from one side of the instrument to the other as the register changes.

The main event is the presentation of the medals. The UK students all do a good job of getting their Union Jacks in front of the competing flags from adjacent competitors. The space in front of the stage turns into a bit of a scrum of photographers. I turn out to be substantially bigger than the average South-East Asian mathematician, and so get some particularly suitable shots of our gold medallists.

During a further long sequence of dancing, everyone starts to drift away back towards the closing dinner at our Irotama hotel. It turns out that the British Maths Olympiad booklets have finally arrived at this late hour. Gabriel and his new friend from the Irish delegation do an excellent job of speedily distributing them amongst all the teams. After a slow start, the dance floor gradually fills while a table of deputy leaders watches on with a mixture of enthusiasm, concern and indifference. Some final goodbyes are said, others plan to chat the whole night away. This year’s IMO draws to a close.

Sunday 28th / Monday 29th July

We leave for picturesque Santa Marta airport after breakfast. It appears that some of the team have spent a non-zero time asleep. The short hop to Bogota is almost entirely made up of mathematicians, and there are plenty of paper pads and Rubik’s cubes out in the departure lounge (remembering of course that compasses can’t be taken in hand luggage).

A short change in Bogota is enlivened when the ever-suspicious Andrew Carlotti is summoned by the police. It turns out to be merely a random inspection… Geoff and I muse over plans for next year, and I learn that The Glass Bead Game is a very useful tool for getting to sleep much earlier than natural.

After a layover and much-needed triple espresso in Madrid, and an initial aborted landing at windy Heathrow, everyone is united with adoring parents and other fans. Despite Geoff’s best efforts, his dream of a flash-heavy welcome by the national press fails to come to fruition. We live in hope for next year.