Hoang Tuy was born to a poor family in the central province of Quang Nam. He was always a high-achieving student, especially in mathematics.

He joined the Indochina War against French after graduating from high school and then worked as a teacher in neighboring Quang Ngai Province. From 1951, he studied a university mathematics program of the Soviet Union on his own and also researched education issues.

Tuy was assigned by the Ministry of Education and Training in 1955 to lead the post-war education reform. He was also in charge of drafting all text books.

In 1956, he taught mathematics at the University of Education, now the Vietnam National University in Hanoi. A year later, he and eight other people were sent to study at the Lomonosov University, now the Moscow State University, where he successfully defended his doctoral theses in maths and physics.

In 1964, he invented a method called "Tuy’s cut" and that was considered the first step for a brand new mathematical discipline: global optimization. In 1997, the Linköping Institute of Technology (Sweden) hosted an international seminar to honor his global optimization work.

Tuy became the first person in the world to receive the Constantin Carathéodory Prize from the International Society of Global Optimization for his pioneering work and fundamental contributions to global optimization in September 2011.

He published over 100 works in renowned international magazines on various areas of mathematics, including many on Math-Net.Ru.

Tuy, with Professor Le Van Thiem, set the foundation for mathematical development in Vietnam. He was head of the Institute of Mathematics in Hanoi for 10 years, after Thiem led it for the first five years.

His son, Hoang Duong Tuan, is now a professor at the University of Technology, Sydney, Australia, where he is working on the applications of optimization in various engineering fields.