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| UK maths prodigy sets out to prove his worth at international Olympiad | |
| (about 3 hours later) | |
| “I’ve always been interested in maths, since I can remember,” says 16-year-old Joe Benton. “I find it elegant. I really enjoy the kick you get when you solve a problem, when it’s something you’ve been thinking of as impossible for a long time, and it suddenly becomes obvious. That ‘a-ha’ moment – it’s fun.” | “I’ve always been interested in maths, since I can remember,” says 16-year-old Joe Benton. “I find it elegant. I really enjoy the kick you get when you solve a problem, when it’s something you’ve been thinking of as impossible for a long time, and it suddenly becomes obvious. That ‘a-ha’ moment – it’s fun.” |
| Joe is one of six gifted young mathematicians chosen for the British team who will compete next week in the 56th International Mathematical Olympiad (IMO) in Chiang Mai, Thailand. The IMO is the world cup of mathematics competitions for secondary school-age students. It began in 1959 with seven countries competing in Bucharest, Romania. Now, it’s a global event with more than 500 teenagers from over 100 countries. | Joe is one of six gifted young mathematicians chosen for the British team who will compete next week in the 56th International Mathematical Olympiad (IMO) in Chiang Mai, Thailand. The IMO is the world cup of mathematics competitions for secondary school-age students. It began in 1959 with seven countries competing in Bucharest, Romania. Now, it’s a global event with more than 500 teenagers from over 100 countries. |
| Like the Olympics, competitors win individual medals but also compete as a national team. The event has its own flag and even its own hymn: “Gathered in one desire / We are coming from everywhere / To share the joy of joining / Science and art in one / We add, we multiply / And we come to a total / Infinite is our dream / With no measure indeed / We shall meet again / Solving the problems / To think is our way / Friendship our system is.” | Like the Olympics, competitors win individual medals but also compete as a national team. The event has its own flag and even its own hymn: “Gathered in one desire / We are coming from everywhere / To share the joy of joining / Science and art in one / We add, we multiply / And we come to a total / Infinite is our dream / With no measure indeed / We shall meet again / Solving the problems / To think is our way / Friendship our system is.” |
| Teams from as far afield as Afghanistan, Trinidad and Tobago, Syria and Mongolia, Macau, Cuba, Cambodia and Iran will descend on Chiang Mai University for the opening ceremony on Thursday. Then on Friday morning Joe and the rest of the British team, fresh from a last-minute training camp in Malaysia, will take their seats alongside their rivals in a vast examination hall. The test lasts four and a half hours and is made up of three problems, each more difficult than the last. The next day the competitors will do the same again. | Teams from as far afield as Afghanistan, Trinidad and Tobago, Syria and Mongolia, Macau, Cuba, Cambodia and Iran will descend on Chiang Mai University for the opening ceremony on Thursday. Then on Friday morning Joe and the rest of the British team, fresh from a last-minute training camp in Malaysia, will take their seats alongside their rivals in a vast examination hall. The test lasts four and a half hours and is made up of three problems, each more difficult than the last. The next day the competitors will do the same again. |
| “The time flies,” says Joe. “You sit there and you think. You have an idea and you try it and you work from there. There’s some anxiety, but that comes mostly after you’ve sat the exams and you’re waiting for the results.” | “The time flies,” says Joe. “You sit there and you think. You have an idea and you try it and you work from there. There’s some anxiety, but that comes mostly after you’ve sat the exams and you’re waiting for the results.” |
| Joe’s state primary school worked hard to keep up with his appetite for maths; his secondary, St Paul’s independent school in Barnes, south-east London, has an established tradition of entering pupils in maths competitions. | Joe’s state primary school worked hard to keep up with his appetite for maths; his secondary, St Paul’s independent school in Barnes, south-east London, has an established tradition of entering pupils in maths competitions. |
| His gift was soon spotted by the UK Mathematics Trust, which runs contests in schools to scout for talent, and when Joe was 14 he enrolled in a summer camp for exceptionally talented young mathematicians. | His gift was soon spotted by the UK Mathematics Trust, which runs contests in schools to scout for talent, and when Joe was 14 he enrolled in a summer camp for exceptionally talented young mathematicians. |
| Since then he has attended training camps and last year he was chosen to represent the UK at the IMO in Cape Town, where he won a silver medal as part of a team that came 20th overall (the top three was China, USA and Taiwan). | Since then he has attended training camps and last year he was chosen to represent the UK at the IMO in Cape Town, where he won a silver medal as part of a team that came 20th overall (the top three was China, USA and Taiwan). |
| “There are obviously countries that are stronger – China, America, Russia,” Joe says philosophically. “It’s natural because of the population size and they put a lot more effort into it as nations.” | “There are obviously countries that are stronger – China, America, Russia,” Joe says philosophically. “It’s natural because of the population size and they put a lot more effort into it as nations.” |
| This year Joe, whose father works for IBM and whose mother is a geneticist, is hoping for gold. “It always works best when you’re enjoying it,” he says. In the runup he’s been doing one or two problems a day, gradually building up as the competition approaches. | This year Joe, whose father works for IBM and whose mother is a geneticist, is hoping for gold. “It always works best when you’re enjoying it,” he says. In the runup he’s been doing one or two problems a day, gradually building up as the competition approaches. |
| “Sometimes I sit at my desk. Sometimes I lie on my bed and stare at the ceiling, trying to think. Sometimes I watch the TV and I’m thinking.” | “Sometimes I sit at my desk. Sometimes I lie on my bed and stare at the ceiling, trying to think. Sometimes I watch the TV and I’m thinking.” |
| Last year, the little-known world of the IMO was the backdrop for a well-reviewed feature film, X+Y, starring Asa Butterfield as a mathematics prodigy who has difficulty understanding people but is very good with numbers. He represents the UK at the IMO, during which there’s a romantic encounter with a fellow competitor, a Chinese girl called Zhang Mei. | Last year, the little-known world of the IMO was the backdrop for a well-reviewed feature film, X+Y, starring Asa Butterfield as a mathematics prodigy who has difficulty understanding people but is very good with numbers. He represents the UK at the IMO, during which there’s a romantic encounter with a fellow competitor, a Chinese girl called Zhang Mei. |
| The film triggered much debate among the world’s best young mathematicians, both for its portrayal of a gifted young “mathlete” on the autistic spectrum and its love interest. In reality “there’s not much romance”, says Joe’s teammate Warren Li, 17, an IMO veteran with two competitions under his belt. | The film triggered much debate among the world’s best young mathematicians, both for its portrayal of a gifted young “mathlete” on the autistic spectrum and its love interest. In reality “there’s not much romance”, says Joe’s teammate Warren Li, 17, an IMO veteran with two competitions under his belt. |
| Indeed, there aren’t many girls. Only 10% of all competitors are female, a situation that organisers are trying to address with the launch of girls-only international contests such as the European Girls’ Mathematical Olympiad. | Indeed, there aren’t many girls. Only 10% of all competitors are female, a situation that organisers are trying to address with the launch of girls-only international contests such as the European Girls’ Mathematical Olympiad. |
| It’s not because of a lack of female talent, says the UK team leader Dr Geoff Smith, of Bath University (played by Eddie Marsan in the film). “Girls can do this. Sometimes the best young mathematician in the world is a girl.” | It’s not because of a lack of female talent, says the UK team leader Dr Geoff Smith, of Bath University (played by Eddie Marsan in the film). “Girls can do this. Sometimes the best young mathematician in the world is a girl.” |
| Lisa Sauermann, from Germany, was the most successful participant in the 2011 IMO and currently ranked second in the IMO hall of fame; last year Maryam Mirzakhani, an Iranian former IMO gold medal winner and now a maths professor, became the first woman to win the world’s most prestigious mathematics prize, the Fields Medal. | Lisa Sauermann, from Germany, was the most successful participant in the 2011 IMO and currently ranked second in the IMO hall of fame; last year Maryam Mirzakhani, an Iranian former IMO gold medal winner and now a maths professor, became the first woman to win the world’s most prestigious mathematics prize, the Fields Medal. |
| On the film’s portrayal of maths prodigies, Smith says: “There has been a natural concern in the maths community that portraying some mathematicians as being less than socially fluent is dangerous, because it could lead to the misapprehension that mathematicians are all strange. | On the film’s portrayal of maths prodigies, Smith says: “There has been a natural concern in the maths community that portraying some mathematicians as being less than socially fluent is dangerous, because it could lead to the misapprehension that mathematicians are all strange. |
| “My personal view is that the prefix ‘mis’ in the previous sentence can be deleted. All mathematicians are strange because they place such an exceptional value on thought, ideas and understanding. I think that the maths community should be proud of the way it embraces people on the basis of their enthusiasm for, and interest in, mathematics. | “My personal view is that the prefix ‘mis’ in the previous sentence can be deleted. All mathematicians are strange because they place such an exceptional value on thought, ideas and understanding. I think that the maths community should be proud of the way it embraces people on the basis of their enthusiasm for, and interest in, mathematics. |
| “Most students are relaxed and outgoing, with the full set of skills that allow them to prosper in the teenage social maelstrom. Some others are not, but everyone gets along almost all of the time, united by a passion for ideas and ingenuity.” | “Most students are relaxed and outgoing, with the full set of skills that allow them to prosper in the teenage social maelstrom. Some others are not, but everyone gets along almost all of the time, united by a passion for ideas and ingenuity.” |
| Each year the UK team is made up of students from a mix of state and independent schools, selective and non-selective. Despite concern among politicians about the overall maths performance of UK pupils in international Pisa tests (Britain ranked 26th in maths out of 65 countries most recently), we hold our own in the IMO. | Each year the UK team is made up of students from a mix of state and independent schools, selective and non-selective. Despite concern among politicians about the overall maths performance of UK pupils in international Pisa tests (Britain ranked 26th in maths out of 65 countries most recently), we hold our own in the IMO. |
| “For our population, we do reasonably well,” says Smith. “The south-east Asian teams tend to dominate. In the last 10 years China, Japan, Singapore, Hong Kong, Vietnam and Taiwan have been very strong. Kids there are expected to put a lot more effort into their school work and academic achievement is more highly prized. Europeans have made a cultural decision that they don’t want to do that. Their idea of childhood is much less driven.” | “For our population, we do reasonably well,” says Smith. “The south-east Asian teams tend to dominate. In the last 10 years China, Japan, Singapore, Hong Kong, Vietnam and Taiwan have been very strong. Kids there are expected to put a lot more effort into their school work and academic achievement is more highly prized. Europeans have made a cultural decision that they don’t want to do that. Their idea of childhood is much less driven.” |
| Smith says the diligence required to master a GCSE or A-level syllabus in maths bears little relation to the sort of creativity and brilliant insight required to excel in an IMO competition. “You can’t teach that,” he says. | Smith says the diligence required to master a GCSE or A-level syllabus in maths bears little relation to the sort of creativity and brilliant insight required to excel in an IMO competition. “You can’t teach that,” he says. |
| “The kids who eventually make the IMO team, they are so smart they stand out like a sore thumb when they are 12, 13 or 14. It’s like the difference between being an Olympic swimmer and being able to do a width.” | “The kids who eventually make the IMO team, they are so smart they stand out like a sore thumb when they are 12, 13 or 14. It’s like the difference between being an Olympic swimmer and being able to do a width.” |
| Warren Li is definitely an “Olympic swimmer” and among the UK’s best hopes for a gold this year. He aimed for gold last year but just missed out. The other team members are Lawrence Hollom, Samuel Kittle, Neel Nanda and Harvey Yau. | Warren Li is definitely an “Olympic swimmer” and among the UK’s best hopes for a gold this year. He aimed for gold last year but just missed out. The other team members are Lawrence Hollom, Samuel Kittle, Neel Nanda and Harvey Yau. |
| “I was probably not as well prepared as I could have been,” says Warren, who studied at a York comprehensive before moving to Eton for sixth form. “This year, I’m aiming for gold again, and this time I’m the most experienced member of the UK team. Maybe I feel a little pressure to be the best. But I really enjoy the whole process. It’s actually fun.” | “I was probably not as well prepared as I could have been,” says Warren, who studied at a York comprehensive before moving to Eton for sixth form. “This year, I’m aiming for gold again, and this time I’m the most experienced member of the UK team. Maybe I feel a little pressure to be the best. But I really enjoy the whole process. It’s actually fun.” |
| Two IMO sample problems | Two IMO sample problems |
| The first was used at the IMO in 2001 and is free of the maths jargon that can hinder non-mathematicians (on the IMO website here): | The first was used at the IMO in 2001 and is free of the maths jargon that can hinder non-mathematicians (on the IMO website here): |
| 21 girls and 21 boys took part in a mathematical contest.(i) Each contestant solved at most six problems.(ii) For each girl and each boy, at least one problem was solved by both of them.Prove that there was a problem that was solved by at least three girls and at least three boys. | 21 girls and 21 boys took part in a mathematical contest.(i) Each contestant solved at most six problems.(ii) For each girl and each boy, at least one problem was solved by both of them.Prove that there was a problem that was solved by at least three girls and at least three boys. |
| And another from 2014 that uses more technical terms (on the IMO website here): | And another from 2014 that uses more technical terms (on the IMO website here): |
| Let n² be an integer. Consider an n x n chessboard consisting of n² unit squares.A configuration of n rooks on this board is peaceful if every row and every column contains exactly one rook. Find the greatest positive integer k such that, for each peaceful configuration of n rooks, there is a k × k square which does not contain a rook on any of its k² unit squares. | Let n² be an integer. Consider an n x n chessboard consisting of n² unit squares.A configuration of n rooks on this board is peaceful if every row and every column contains exactly one rook. Find the greatest positive integer k such that, for each peaceful configuration of n rooks, there is a k × k square which does not contain a rook on any of its k² unit squares. |
| The solutions are on the IMO website here. Good luck. | The solutions are on the IMO website here. Good luck. |