TPO - In 50 years of participating in the International Mathematical Olympiad, Vietnam has had 3 math problems selected for inclusion in the exam. These were in 1977, 1982, and 1987.
On August 10th, the Institute for Advanced Studies in Mathematics, in collaboration with the Vietnam Mathematical Society, organized a series of activities to commemorate the 50th anniversary of Vietnam's participation in the International Mathematical Olympiad (IMO, 1974-2024). These events included a workshop on evaluating the training and results of national and international mathematics competitions for gifted students from 2015-2024; a panel discussion on building and nurturing a team of young domestic experts and attracting talented Vietnamese people abroad to contribute to national development; and a gala celebrating 50 years of Vietnam's participation in the IMO.
 |
From left to right: Professor Ngo Bao Chau, the first and only Vietnamese person to date to win the Fields Prize (Nobel Prize in Mathematics); Assoc. Prof. Dr. Nguyen Thu Thuy, Director of the Higher Education Department, Ministry of Education and Training; Dr. Pham Tuan Huy, Gold Medalist at IMO 2013 and 2014, currently a Clay Research Fellow at Stanford University, USA; Assoc. Prof. Dr. Nguyen Phi Le, Director of the International Center for Artificial Intelligence Research, Hanoi University of Science and Technology, Silver Medalist at IMO 2000; Pham Kim Hung, CEO of True Platform Joint Stock Company, Gold Medalist at IMO 2004 and Silver Medalist at IMO 2005, at the seminar on Building and Nurturing a Team of Young Experts in the Country and Attracting Talented Vietnamese Human Resources Abroad to Contribute to National Development. |
Before the discussion on building and nurturing a team of young domestic experts and attracting talented Vietnamese people abroad to contribute to the country's development, Dr. Trinh Thi Thuy Giang, Deputy Director of the Institute for Advanced Studies in Mathematics, shared some interesting information about Vietnam's 50-year history of participation in the IMO.
Notably, in 1977, 1982, and 1987, Vietnam had questions included in the official IMO exam.
Professor Vu Hoang Linh, Rector of the Faculty of Natural Sciences , Vietnam National University, Hanoi, and President of the Vietnam Mathematical Society, informed that in the 1977 IMO, exam paper number 2, submitted by the late Associate Professor Phan Duc Chinh, contained the following information:
"In a finite sequence of real numbers, the sum of any 7 consecutive terms is negative, and the sum of any 11 consecutive terms is positive. Determine the largest number in the sequence."
The late Associate Professor Phan Duc Chinh was one of the first teachers of Vietnam's first specialized mathematics class (Specialized Mathematics Class A0, Course 1, formerly the University of Hanoi and later the University of Science, Vietnam National University , Hanoi ). He trained many talented students who won international mathematics medals and also wrote and translated many classic mathematics textbooks in Vietnam.
Speaking about the late Associate Professor Phan Duc Chinh, Professor Tran Van Nhung, former Deputy Minister of Education and Training and a Vietnamese mathematician, said that Professor Chinh served as the deputy head of the Vietnamese student delegation to the IMO in 1974-1976 (the head of the delegation was teacher Le Hai Chau) and as the head of the delegation in 1994, 1996, and 1997.
In 1982, a math problem by the late Associate Professor Van Nhu Cuong was also included in the IMO exam. According to mathematicians, the original problem by the late Associate Professor Van Nhu Cuong was presented as follows:
"Once upon a time (in Nghe An province), there was a square village with each side measuring 100 km. A river ran around the village. Every point in the village was no more than 0.5 km from the river (*).
Prove that there are two points on the river whose distance as the crow flies is no more than 1 km, but the distance along the river is no less than 198 km.
(Let's assume the river has negligible width.)
The Vietnamese problem was very difficult and unique. Many countries wanted to remove it from the exam. But the President of the IMO that year, Professor and Academician R. Alfred, Director of the Institute of Mathematics, Hungarian Academy of Sciences, praised it and decided to keep it. Later, this problem became question 6 of the 1982 IMO exam and was revised as follows:
Let S be a square with side length 100, and L be a non-self-intersecting polygonal line formed from line segments A0A1, A1A2…,An-1An with A0#An. Assume that for every point P on the boundary of S, there exists a point in L at a distance of no more than 1/2 from P. Prove that there exist two points X and Y belonging to L such that the distance between X and Y does not exceed 1, and the length of the polygonal segment L between X and Y is not less than 198.
Only 20 contestants in the competition were able to solve this problem. Among them was Le Tu Quoc Thang from the Vietnamese team. He also won the Gold Medal with a score of 42/42, and the Vietnamese team ranked 5th out of 30 participating countries. Le Tu Quoc Thang is currently a Professor at the Georgia Institute of Technology, USA.
The third problem from Vietnam included in the 1987 IMO exam was by Dr. Nguyen Minh Duc, with the following content:
"Prove that there does not exist a function f: R₁→R₁, where R₁ is the set of non-negative integers, such that: f(f(n)) = n + 1987 for all n".
Interestingly, Dr. Nguyen Minh Duc is a former student of the High School for Gifted Students in Natural Sciences, who won a Silver Medal at the IMO in 1975, the second year Vietnam participated in this international competition.
The International Mathematical Olympiad (IMO) has been held in Romania since 1959. Vietnam began participating in 1974 and has since sent teams 48 times with 288 contestants (including 18 female contestants), achieving 271 medals (69 gold medals, 117 silver medals, and 85 bronze medals). The medal rate for Vietnamese students is 94%. Throughout its 50-year history, 10 students have achieved perfect scores, and 10 students have won two gold medals. In terms of unofficial team performance, the Vietnamese team has consistently ranked in the top 10 worldwide in most of its participation years.
The IMO is a source of pride for families, teachers, and the high schools and provinces whose students participate. Notably, the High School for Gifted Students in Natural Sciences, Faculty of Natural Sciences, Vietnam National University, Hanoi, has won 82 medals (32 Gold, 32 Silver, and 18 Bronze) since 1974, accounting for nearly 30% of the total medals won nationwide in this competition.
In 2017, Vietnam achieved its best performance ever (ranking third in the world), with 4 Gold medals, 1 Silver medal, and 1 Bronze medal.
Source: https://tienphong.vn/3-bai-toan-cua-viet-nam-trong-de-thi-olympic-toan-hoc-quoc-te-post1662683.tpo
