On August 10, the Institute for Advanced Study in Mathematics in collaboration with the Vietnam Mathematical Society organized a series of activities to celebrate 50 years of Vietnam's participation in the International Mathematical Olympiad (IMO, 1974-2024) including events such as the Workshop on Evaluation of training and results of national and international math competitions for excellent students in the period 2015-2024; discussion: Building and nurturing a team of young domestic experts and attracting talented Vietnamese human resources abroad to contribute to the development of the country; gala to celebrate 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 Medal (Nobel Prize in Mathematics); Associate Professor, Dr. Nguyen Thu Thuy, Director of the Department of Higher Education, Ministry of Education and Training; Dr. Pham Tuan Huy, Gold Medal IMO 2013 and 2014, currently a Clay Researcher at Stanford University, USA; Associate Professor, Dr. Nguyen Phi Le, Director of the International Research Center for Artificial Intelligence, Hanoi University of Science and Technology, Silver Medal IMO 2000; Pham Kim Hung, CEO of True Platform Joint Stock Company, Gold Medal at IMO 2004 and Silver Medal at IMO 2005 at the seminar Building and fostering a team of young domestic experts and attracting talented Vietnamese human resources abroad to contribute to the development of the country.

Before entering the discussion on building and nurturing a team of young domestic experts and attracting talented Vietnamese human resources abroad to contribute to the country's development, Dr. Trinh Thi Thuy Giang, Deputy Director of the Institute for Advanced Study in Mathematics, gave some interesting information about the 50-year history of Vietnam's participation in IMO.

It is noteworthy that in 1977, 1982, and 1987, Vietnam had entries in the official IMO exam.

Prof. Dr. Vu Hoang Linh, Principal of the University of Natural Sciences, Vietnam National University, Hanoi, President of the Vietnam Mathematical Society, informed that at the 1977 IMO exam, exam number 2 was by the late Associate Professor Phan Duc Chinh with the following content:

"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 among the terms of the sequence".

The late Associate Professor Phan Duc Chinh was one of the first teachers of the first Math Specialized Class in Vietnam (Math Specialized Class A0, Course 1, former General University and later University of Natural Sciences, Vietnam National University, Hanoi), participated in training many excellent students who won international Math medals and was also the one who wrote and translated many classic Math textbooks in Vietnam.

Speaking about the late Associate Professor Phan Duc Chinh, Professor Dr. Tran Van Nhung, former Deputy Minister of Education and Training, a Vietnamese mathematician, said that Mr. Chinh was the Deputy Head of the Vietnamese Student Delegation to attend IMO in 1974-1976 (Head of the Delegation was teacher Le Hai Chau) and was 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:

"In the past (in Nghe An) there was a square village with each side of 100km. There was a river running around the village. Any point in the village was no more than 0.5km away from the river (*).

Prove that there are 2 points on the river whose distance as the crow flies is not more than 1 km, but the distance along the river is not less than 198 km.

(We assume the river has negligible width).

Vietnam's problem was very difficult and unique. Many countries wanted to remove it from the exam. But the President of IMO that year, Professor, Hungarian Academician R.Afred, Director of the Institute of Mathematics, Hungarian Academy of Sciences, praised it and decided to keep it. Later, this problem was 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-intersecting zigzag line formed by line segments A0A1, A1A2…,An-1An with A0#An. Suppose that for every point P on the boundary of S there is a point in L that is no more than ½ away from P. Prove that: There exist 2 points X and Y in L such that the distance between X and Y does not exceed 1, and the length of the zigzag line L between X and Y is not less than 198".

Only 20 contestants of the competition were able to solve this test. Among them was Le Tu Quoc Thang from the Vietnamese delegation. He also won the Gold Medal with a score of 42/42, while the Vietnamese delegation ranked 5/30 participating countries. Le Tu Quoc Thang is currently a professor at the Georgia Institute of Technology, USA.

The third Vietnamese problem included in the IMO exam in 1987 was by Dr. Nguyen Minh Duc with the following content:

"Prove that there does not exist a function f: R₁→R₁, R₁ is a 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 the Gifted in Natural Sciences, winning a Silver Medal at the IMO in 1975, the second year Vietnam participated in this international arena.

IMO is the pride of families, teachers, and high schools and provinces whose students participate. A typical example is the High School for the Gifted in Natural Sciences, University of Natural Sciences, Vietnam National University, Hanoi, which has won 82 medals since 1974 (32 Gold Medals, 32 Silver Medals, 18 Bronze Medals), accounting for nearly 30% of the total number of medals nationwide in this competition.

In 2017, Vietnam had its best ever performance (ranked third in the world), with 4 Gold Medals, 1 Silver Medal and 1 Bronze Medal.

Nghiem Hue