Sri Lanka’s dream of winning a silver medal or gold medal at the International Mathematical Olympiad

59th International Mathematical Olympiad (IMO) was held in Cluj-Napoca, Romania during July 3 – 14, 2018. 594 contestants from 107 countries participated in the event. The US team came top at this competition with 5 gold medals and 1 silver medal. Russia and China came second and third with 5 gold medals and 1 silver medal, and 4 gold medals and 2 silver medals respectively. The International Mathematical Olympiad is the most prestigious mathematical competition for high school students. A country can send up to 6 school students under 20 years of age to the IMO and they have to solve 6 problems in 9 hours over two days. Many IMO medal winners who chose mathematics as their career have become notable mathematicians including Fields medal winners. Fields medal is the equivalent of Nobel Prize in mathematics.

Winning a silver medal or a gold medal at the International Mathematical Olympiad is a great achievement for a student with a passion for mathematics. For such an achievement natural talent in mathematics is a must but it is not sufficient. A student should have an intrinsic motivation for mathematics and solve mathematical Olympiad type problems frequently. For a country winning a silver medal or a gold medal at the IMO is prestigious and it is a sign of a substantial percentage of young school children in the country solving mathematical problems outside the school mathematics curriculum. Just the school mathematics is not enough to develop school children’s mathematical abilities. In school mathematics school children learn mathematics inside a box that restricts the methods used and topics discussed. For example recreational mathematics has no place in school mathematics. In Olympiad mathematics, the mathematics of the IMO and similar competitions, there is no such box. Consider the following problem # 4 given in this year’s IMO:

A site is any point ) ,( y x in the plane such that x and y are both positive integers less than or equal to 20. Initially, each of the 400 sites is unoccupied. Amy and Ben take turns placing stones with Amy going first. On her turn, Amy places a new red stone on an unoccupied site such that the distance between any two sites occupied by red stones is not equal to 5. On his turn, Ben places a new blue stone on any unoccupied site. (A site occupied by a blue stone is allowed to be at any distance from any other occupied site.) They stop as soon as a player cannot place a stone. Find the greatest K such that Amy can ensure that she places at least K red stones, no matter how Ben places his blue stones.

Solving this problem does not require any specific mathematical knowledge. Only a high level of mathematical thinking and some creativity are required. This is a problem in Combinatorics. IMO problems come from 4 topics – Number Theory, Algebra, Geometry and Combinatorics. Combinatroics problems have to be solved mostly from first principles and Sri Lankan students struggle in these type of problems. For this problem only Maneth Perera and Gaura Mahabaduge were able to get any marks, 2 and 7 respectively. Other 4 got zero marks. Gaura won a bronze medal with 18 points. Our Sri Lankan team won 1 bronze medal and 3 honorable mention awards. An honorable mention award is given for a perfect score of 7 for a problem if a medal is not won. Sri Lanka with 47 points was placed at 72nd place.

Even though Sri Lanka has been winning bronze medals regularly at the IMO since the introduction of the Sri Lankan Mathematics Competition (SLMC) for IMO team selection in 2004, our country has never won a silver medal or a gold medal. In 2004 the Sri Lanka Olympiad Mathematics Foundation (SLOMF) was formed by some university academics as a non-profit organization to popularize mathematics among school children. The SLOMF introduced the Sri Lankan Mathematical Olympiad (SLMO) in 2004 which consists of the SLMC and the Sri Lankan Mathematics Challenge Competition (SLMCC). The SLMC is a competition consisting of MCQ questions that introduces Olympiad mathematics. The SLOMF with its limited financial and human resources had to work hard to get to the level of winning bronze medals regularly at the IMO. But winning silver or gold medals at the IMO seems to require even more effort.

In 2004 the ministry of education started sending teams to the International Mathematics and Science Olympiad (IMSO), a regional Olympiad competition participated by about 25 countries for grade 6 students. Also, the ministry of education started sending teams to the International Mathematics Competition (IMC), another regional Olympiad competition participated by about 30 countries, in 2011 after the Sri Lanka Olympiad Mathematics Foundation started sending teams to this competition in 2010. The International Mathematics Competition (IMC) is held at two levels: Category II for grades 7 and 8 students and category III for grades 9, 10 and 11 students. The ministry of education selects teams for category II level, and the ministry of education and the SLOMF select teams for category III level. The International Mathematical Olympiad is open for any school student under 20 years of age. The SLOMF selects teams to the IMO.

The ministry of education has spent considerable amount of money into the IMSO and the IMC programs. The Sri Lanka Olympiad Mathematics Foundation (SLOMF) does not have any government support and it has carried out its work of conducting the SLMO and selecting and training teams to the IMC and the IMO with the help a of lot of volunteers in the foundation. But it has to pay for outsourced services such as conducting the Sri Lankan Mathematics Competition (SLMC) by the Sri Lanka Department of Examinations.

One would expect that with the government funded international Olympiad mathematics competitions for students in grades 6 – 11 for more than 15 years the country should be winning silver and gold medals at the IMO. But it seems that the causes for the failure are many and deep rooted. When Bangladesh, a country that was performing below Sri Lanka in 2005, won a gold medal at the IMO this year it is time for the Sri Lanka Olympiad Mathematics Foundation (SLOMF) to try harder with its limited resources.

As a first step the SLOMF is going to start publishing the SLMC Problem of the Week, a weekly math problem, in www.slmathsolympiad.org from September 12th. The first problem is an easy combinatorics problem similar to the IMO problem given above. Also, from the next year the SLOMF is going to hold the Sri Lankan Mathematics Competition at the following three levels: SLMC 8 for grades 6-8, SLMC 11 for grades 6-11 and SLMC 13 for grades 6-13. The idea is a gradual progression through interesting puzzle type questions out of the school mathematics curriculum box to Olympiad mathematics. Though the country has not won silver or gold medals at the IMO yet the exposure our students to Olympiad mathematics has already made the country visible in the world mathematical community. Dr. Uditha Nalin Katugampola, who got selected to the IMO team in 1997 but couldn’t go to the IMO because there was no money to send a team to the IMO that year and who worked tirelessly for the SLOMF during 2003 – 2005, has done research for his PhD in mathematics and come up with a new field of mathematics that bears his name – Katugampola Fractional Calculus. He has also received a US$ grant of 300, 000 for his research. Currently he works as an assistant professor of mathematics at Florida Polytechnic University. It is hoped that Olympiad mathematics will be instrumental in getting the due place for mathematics in the country’s education in the near future.