"'Nobel Prize of Mathematics' Professor Heo Jun-yi: 'Math Dropouts Should Not Be Intimidated' [Reading Science]"

"Study Broadly and Find Enjoyment in Learning Independently"
"Consider Why Many Mathematicians Around the World Are Drawn to Mathematics"
"My Research Results Enable Many Previously Impossible Calculations"
"Chose U.S. Citizenship at Ages 16-17, No Korean Citizenship"

[Asia Economy Reporter Kim Bong-su] Heo Jun, the first Korean to win the Fields Medal, known as the 'Nobel Prize of Mathematics,' held his first official press conference after returning to Korea on the afternoon of the 13th at the Korea Institute for Advanced Study (KIAS) in Hongneung, Seoul. Once almost a 'supoja' (a student who gives up on math), he advised Korean students facing the 'supoja' crisis, saying, "Don't be too discouraged; study broadly and in ways that bring you joy," and added, "Remember that many mathematicians and students around the world are fascinated by the joy of mathematics, and reflecting on why that is can be helpful." To adults, he also urged, "Please create policy frameworks so that students' courage is not betrayed." Meanwhile, in response to Asia Economy's question about when he chose American citizenship, Professor Heo revealed, "I made the choice when I was 16 or 17." He did not answer regarding plans to regain Korean citizenship. It is known that Professor Heo was born in the U.S. while his parents were studying there, returned to Korea at age two, held dual citizenship, and later chose American citizenship.

Below is a Q&A with Professor Heo.

- About one-tenth of Korean students are 'supoja.' What advice would you give?

▲ That's a difficult question. The biggest problem is that students' precious time is used not for learning but for evaluation. I think this is due to the socio-cultural background where one must win in competition and be more perfect rather than focusing on mathematics or the educational process. I am not an expert as I haven't deeply considered this before higher education. I can't speak in depth. However, I want to tell students not to be too discouraged and to study broadly in ways that bring them joy rather than trying to be perfect without mistakes. To adults who can immediately change policies such as social organizations, I ask that you create policy frameworks so that students' courage is not betrayed and good results can come out.

- Do Korean students study math too much, or too little, causing problems?

▲ The answer depends on which group you consider. I have lectured at relatively top universities like Stanford and Princeton in the U.S., where students come from various countries and cultural backgrounds. Among them, there are many Korean students. Contrary to common belief, Korean students are not that well-prepared. They are excellent at solving problems quickly within a narrow scope, but they are relatively less prepared for broad and deep study. I hope that the system in high school is well established so that students are well-prepared to study deeply after choosing their majors in university.

- How are the research achievements that led to your award specifically applied in industry?

▲ I am a pure mathematician among pure mathematicians. It's hard to answer perfectly. What I know is that (the research achievements) can be used to create algorithms that calculate quantities that were previously difficult to compute more quickly. Things that were previously uncomputable can now be computed, and in that sense, they can be applied.

To use an analogy, nowadays writing is natural and not considered difficult; everyone can do it. But 500-600 years ago in the medieval era, writing and reading were processes that only a few could go through with difficulty. Pure mathematics today is at a similar stage. If you asked a medieval scholar who argued that it was important for lords to write and read whether universal literacy could help prepare for next year's poor harvest or drought, it would be difficult to answer. It's a similar situation. In the long term, to solve the technical parts to maintain minimum production regardless of drought, a large cultural framework must be established. If you ask in a few sentences whether this or that can be done, I can give a long answer, but it's difficult to summarize in two or three sentences in this setting.

- Please explain your research achievements in simple terms.

▲ It's hard to explain what it is, and in fact, the explanation may not be that important. Interestingly, the Hodge structure found by the British mathematician Hodge in geometry is hidden behind combinatorics, algebra, analysis, and other subjects. Many mathematicians, including myself, have uncovered this over the past 20-30 years. The puzzling question is whether there exists a perfectly identical pattern behind different mathematical objects. It's a huge problem, and it's difficult to provide a neat answer within one or two generations. Just the observation of the existence of such patterns is exciting and thrilling. It's fascinating and fun that a great discovery awaits us.

- Are the results of pure mathematics research discoveries or inventions?

▲ This is one of the old questions. Pure mathematics, unlike science, does not rely on experiments or external observations but is a structure created by interactions among different minds. Therefore, it is easy to think of it as a discovery rather than an invention. However, considering that independent minds repeatedly find the same structures historically, it's hard to believe it's mere coincidence. As a participant in mathematical activity, sometimes it feels more like a discovery than an invention.

- You are giving a lecture today on boundaries and relations. What will it be about?

▲ Come and listen to the content. I chose the topic because I thought it would be interesting to share my feelings about these two words from the perspective of someone doing mathematics, aiming for a subject that non-mathematicians could enjoy and understand meaningfully to some extent.

- What is your secret to immersing yourself in work you like?

▲ This is also a problem I have pondered for a long time. Generally speaking, when I think about what worked for me, when things don't go well and I want to like something, I end up not liking it and find it hard to maintain a pure heart. I hope to help myself, give myself space, and wait. Not only when others pressure you but also when you pressure yourself, it's hard to like something with a pure heart. There are times to give up and times to rest, and if you encourage yourself, good results may come.

- You are the first Fields Medalist in combinatorics. Do you think "everything is combinatorics"?

▲ Geometers say everything is geometry, analysts say everything is analysis, and algebraists say everything is algebra. From a combinatorialist's perspective, to defend myself, it is the study of the most fundamental objects. It is a field of mathematics emphasizing primal characteristics that can always be computed by computers and explained to anyone. Modern mathematics has developed so much that explaining the core problems of analysis, algebra, and geometry to students requires 5-6 years of graduate training. The only exception is combinatorics. The important open problems and what is not understood in this field can be conveyed even to first-year undergraduates. Because of this directness and simplicity, combinatorialists consider it more primal than other fields. Difficult problems in other fields can ultimately be reduced and solved through combinatorics.

- You mentioned solving math problems with your eight-year-old son. What is your secret to studying math with children?

▲ It's not really studying math, but I solve one math problem a day with my eldest son. He creates a problem each day, I solve it, and he grades it. The problems are not difficult; he brings problems he saw at school, like counting how many circles are drawn. Since I solve them too easily, now he draws much more complicated ones. I struggle painfully and sometimes make mistakes. Through this process, he learns the concept of multiplication. As a novice parent, I am learning too.

- What has Korea done for you, Professor Heo?

▲ (Choi Jae-kyung, Director of KIAS) Before studying abroad, he completed elementary school through master's degree in Korea. There were many ups and downs, including dropping out of high school. I consider the dropout itself as something Korea did for Professor Heo. People say Korea's education has many problems and needs fixing, but I heard similar problems exist in the U.S. and U.K. It's a story of a mathematical genius suffering because of poor educators. This happens in developed countries too. After earning his master's degree, Professor Heo conducted research at Princeton and also at KIAS. KIAS is a place for free, curiosity-driven research. I believe the research here helped him a lot.

▲ (Professor Heo) As I said upon returning, I have walked a winding but fastest path. That is the path I have lived, and I spent the first half of my life in Korea. Since I learned most of what I know within or near the educational system during that time, it's hard to imagine what else could have been possible. The experiences I accumulated made me who I am. If it had been a different route, that person would not be me.

- How can one feel the charm of mathematics?

▲ Sorry for repeating, but this is also a difficult question. I fully understand that many students did not find math fun for a long time during school and thought it was a stressful subject. If I could meet my younger self then, I would tell him this fundamental story. There are many mathematicians and math students in the world who enjoy math greatly. Most pure mathematicians live researching daily because they find the act itself very enjoyable. Recognizing that other humans, the same species, are captivated by the charm of math and that their number is large, I hope you occasionally ponder, "Why is that? In what way can it be so attractive?" Then, when you are ready, you too can feel that charm.

- How did you overcome difficulties when solving mathematical problems?

▲ Mathematics is difficult, so it is enjoyable. Like enjoying a marathon that requires long jumps, you train and participate every year. If math were easy, it wouldn't be fun. Because it is difficult and constantly tests how deeply I can think, it is enjoyable. If overwhelmed by temporary stress, you cannot feel joy. Be kind to yourself, rest when you need to, and do it when you are ready. If you exercise beyond your physical capacity, you get injured. Similarly, maintain your curiosity and steadily train at a level where you can grow without injury.

- The math field lacks jobs, and mathematicians are disappearing.

▲ The country and various routes support basic science and mathematics, which is encouraging and appreciated. However, the easiest support is for postdoctoral researchers for 2-3 years. After that period, postdocs have no stable, permanent positions to find real jobs. Therefore, during postdoc years, they cannot conduct long-term research projects but must focus on short-term projects aiming for faculty appointments within three years, writing papers within one year and publishing within another. Hence, I hope more long-term stable jobs are created so that especially young researchers can conduct research with a long-term perspective.

- When did you choose American citizenship?

▲ I chose it when I was 16 or 17. I do not have Korean citizenship.

- Do you plan to regain Korean citizenship?

▲ (Shakes head with a somber expression).