Professor Nguyen Trong Toan: The study of mathematics is met with skepticism due to a lack of practical connection.

A Vietnamese mathematician in the US says a shortcoming in mathematics education in Vietnam is the lack of connection between theory and practice, leading the public to doubt the benefits of studying mathematics.

Professor Nguyen Trong Toan, 42 years old, from Dak Lak province, is a former student of the University of Science , Vietnam National University Ho Chi Minh City, holds a master's degree from the University of Texas, and a doctorate from Indiana University, USA. He previously taught at Brown University and currently teaches at Pennsylvania State University.

In 2018, he received the Centennial Fellowship from the American Mathematical Society, and later the T. Brooke Benjamin Award from the International Society for Industrial and Applied Mathematics (SIAM). This award is given every two years to individuals with outstanding research on nonlinear waves. In 2022, he was appointed a full professor at Pennsylvania State University.

During his visit to Vietnam to attend the 10th National Mathematics Conference in early August, the Professor of Mathematics shared his views on the current methods of teaching and learning mathematics.

Professor Nguyen Trong Toan. Photo: Provided by the subject. — Professor Nguyen Trong Toan. Photo: *Provided by the subject.*

- What are your impressions of the mathematics scene in the country after returning home this time?

- Attending the conference with the participation of nearly 1,000 mathematicians, I am very pleased to see the development of mathematics education in the country, and the efforts of my colleagues in affirming the position of Vietnamese mathematics in the world . In particular, the cohesion within the mathematics community, regardless of region, both domestically and internationally, was clearly evident at the recent Congress.

- In teaching mathematics at the high school level, many people believe that Vietnamese students are good at difficult math problems, learning in a rooster-like way without being able to apply their knowledge. What are your thoughts on this?

- Coming from a family of coffee farmers and never having attended a specialized school or a gifted student exam preparation class, I have always appreciated the efforts of families and schools in teaching.

Some might argue that Vietnamese students only do math like prodigies, without clear practical application, because most high schools focus on teaching students to solve difficult problems and do math quickly. However, it is precisely because of this teaching method that we consistently achieve high rankings in regional and international math competitions every year. Who says this isn't an achievement?

Every time I hear about your outstanding achievements that bring glory to Vietnam, I feel very proud. But why can't we go further than just competing in tournaments?

In my opinion, the direction of development will determine the corresponding goals. I think what students lack is critical thinking. They only focus on solving math problems using the methods they've been taught, without ever considering that they themselves are their best teachers. They should ignite their own passion and desire to learn; we are merely the torchbearers guiding them.

- Minister Nguyen Kim Son said that teaching mathematics should be something students enjoy and feel the need to learn. According to him, what aspects of mathematics teaching and learning should be improved at the secondary level, and how should it be taught and learned effectively?

- I think the shortcoming in teaching and learning mathematics in Vietnam is the lack of connection between theory and exercises in school and real-world situations. This leads to skepticism about learning mathematics. Students haven't found a connection to reality, so their self- discovery thinking hasn't been stimulated.

In the US, elementary school students are introduced to practical math problems, such as those related to electricity and water usage, oil and gas, economics, and engineering. These problems are not designed to trick students but rather to help them understand how life works, thus fostering early cognitive and critical thinking development.

The program is also very flexible and supportive, allowing students with a passion for mathematics to participate. Students in grades 6 and 7 can also join the advanced math program alongside students in grades 9 and 10. Students can create similar problems themselves and find solutions different from those provided by the teacher. This helps them develop their creative thinking and independent spirit.

Professor Nguyen Trong Toan received the T. Brooke Benjamin Prize from the International Society for Industrial and Applied Mathematics (SIAM) in 2022. Photo: Provided by the subject. — Professor Nguyen Trong Toan received the T. Brooke Benjamin Prize from the International Society for Industrial and Applied Mathematics (SIAM) in 2022. Photo: *Provided by the subject.*

So, in your opinion, what is the purpose of studying mathematics?

- If I say that studying mathematics contributes to the development of humanity, would people believe me?

In my opinion, mathematics is the thinking, the vision, and the foundation of all disciplines in the past, present, and undoubtedly the future. Because only mathematics is not bound by rules and external influences, we are free to explore and connect other fields by asking questions to satisfy human curiosity. This freedom has allowed us to discover surprising new theories in physics, chemistry, biology, economics, computer science, and other sciences. This is why mathematics deserves such respect.

Just like when building a house, the bigger and taller the house, the stronger and more solid the foundation must be. Do you want to build a single-story house, a villa, a building, a city, a country, or an entire generation? Do you want to finish your studies, get a job, earn money, and see rapid change? It's like building a single-story house – short-term results, immediate outcomes.

What we want to do is change the times, change the future, introduce new ways of thinking and research directions. We will continue what previous generations of teachers couldn't accomplish. What we left unfinished, our students and future generations will complete. Big goals require a long time. Although we may not see immediate results, I believe that humanity's understanding will gradually change in the future. To make a significant impact, we must have a solid foundation in mathematics.

Mathematics is not just a language, but also a science. The brilliant scientist Albert Einstein once said that progress in mathematics is the prerequisite for new achievements in natural sciences. In fact, all physical phenomena are explained through partial differential equations – one of my main research areas. Closer to home are practical mathematical problems such as data analysis, which require the integration of calculus, geometry, and probability and statistics… I believe that future technological revolutions will continue to depend on the development of mathematics.

- In the US, what kinds of jobs do people with a math degree typically do, and how does their income compare to other professions?

In the US, mathematics graduates can continue their careers in research, becoming university professors or working for companies like Wall Street firms, Facebook, Google, data science research companies, oil and gas companies, etc.

Mathematics is about thinking and vision. If you have good thinking skills and an unconstrained vision, you can achieve anything you want. In my world, mathematics is a bridge connecting the whole world.

Of course, professors' salaries aren't high, only about a quarter of what people working in industrial companies earn, but in return, we get paid and welcomed all over the world, have flexible working hours, plenty of vacation time, and are respected by everyone.

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