Since the launch of Hang Lung Mathematics Awards (HLMA) in 2004, over 2,200 secondary school students in Hong Kong have participated in the competition, and HLMA has nurtured a cadre of young mathematics talents. After completing their studies at leading local or international universities, many have made remarkable achievements in academia and other professions. *Connections* has invited some winners to recount their HLMA experience, and reflect on how HLMA has inspired and influenced their development.

We will begin this series by interviewing Prof. Yin-tat Lee and Dr. Brian Chung, Silver Award winners in 2008 and 2010, respectively. After completing mathematics in their undergraduate studies, Yin-tat earned his doctorate degree at the Massachusetts Institute of Technology, whereas Brian earned his doctorate degree at the University of Chicago. Yin-tat is now an associate professor in the School of Computer Science and Engineering at the University of Washington, with a research interest in algorithms. Brian is currently a postdoctoral research fellow at the Einstein Institute of Mathematics at The Hebrew University of Jerusalem, with a focus on dynamical systems.

C: *Connections*

L: Yin-tat Lee

B: Brian Chung

**C: Have you always loved mathematics? How did it all begin?**

L: I first came across Mathematics Olympiad when I was in Primary Five. I was given training for the competition, and even had the chance to represent my school and compete on the Mainland. Perhaps it was that competition and the thrill of winning that made me fall in love with mathematics.

B: I have two elder brothers who are keen in mathematics, and this is probably why I was able to learn mathematics beyond the school syllabus for my age group. In addition, my primary school teacher granted me the chance to skip a grade and join the school mathematics team, where I could challenge myself and learn mathematics with my senior schoolmates. That was how my passion for mathematics started.

**C: Why did you choose to join HLMA?**

L: I initially planned to find a summer job after finishing the HKCEE, but later I came

across HLMA and was attracted by the generous prizes. At the encouragement of my elder brother, I joined the competition.

B: My eldest brother participated in the inaugural HLMA. At that time, he often invited his teammates back home to discuss their project. Despite being little back then, I found their discussions interesting, so I decided to participate in the 2008 HLMA when I was in Form Four. I didn’t win any award then, but the process was a valuable experience. When I made my second attempt in Form Six and participated in the 2010 HLMA, I won the Silver Award.

**C: How is HLMA different from other mathematics competitions?**

L: HLMA offers students a high degree of flexibility, and the process is very similar to what we do in academic mathematics research. One has to first decide on a research question and then try to solve it; it is really challenging. In fact, my performance in other math competitions was not as brilliant as what I had achieved in HLMA. The skills required here are quite different from other competitions, which laid the foundation for my future career in mathematics research.

B: Unlike other competitions that require contestants to solve a series of preset problems within a limited timeframe, HLMA spans over a year. This competition format offers much latitude and breadth, which is quite new among secondary school students. In conventional mathematics competitions, the questions are always solvable, no matter how difficult they are. Mathematics research is a completely different matter – you can consult experts, but they may not have definite answers. In the end, you still need to think on your own and conduct the research by yourself. It is even possible that there is no result or only partial results after spending months on your research. I would say that this is what makes the HLMA stand apart from other competitions.

**C: What difficulties did you encounter when participating in HLMA? How did you overcome them?**

L: My teammates and I did not have much support when we participated in the competition. We had absolutely no idea how to conduct mathematics research, so it was rather difficult for us to choose a research topic. We then read *Information Theory, Inference and Learning Algorithms* by Prof. David J.C. MacKay, and we came across an interesting chapter about file compression, which we were surprised to learn involves mathematical theories. Inspired by this, we selected a research topic that was related to file compression. Later, when I was studying at university, I found out that someone had already worked on our research topic, and the person was a renowned mathematician. Of course, the mathematician’s research results were more sophisticated and comprehensive than ours, but we were still very happy that we shared a common line of thought, and that our efforts were indirectly affirmed by a leading scholar.

B: After deciding on the research topic, I drew an outline for the research report. I planned to write five chapters, with the first chapter being the background introduction and explanation of the research topic. It went smoothly at first, but I encountered problems in the following chapters, and it became so complicated that I could not tackle them for more than six months. With the submission deadline looming in August, I was still stuck in Chapter Two by April and May, without a clue as to how to proceed, and I contemplated whether or not I should give up. One day, when I was traveling home on a minibus and thinking about the research topic, some ideas suddenly occurred to me. After repeated deliberations and verifications, they were later found to be feasible, and I eventually managed to complete my research report. Even now I still find my research results quite satisfactory.

**C: Can you share with us more about your current research?**

L: My current research is in “Optimization problems”, which means to select an optimal solution from a list of feasible ones. Indeed, the concept of optimization is seen everywhere in our lives; for example, what aircraft shape would save the most fuel, or which components can be installed in a computer processor to offer the best power efficiency, and so on. Although our research findings are still in the theoretical stage, they do have a positive impact on the direction and methods of our future research.

B: I am now mainly working on the research of dynamical systems. The concept can be illustrated by a weather-simulation model that can generate drastically different results when you input variables with only very little difference. For example, if you set the value of x be 0.0123 in the system, the result might be fine weather, but if the value of x is just slightly different, perhaps 0.012301, then the result might be a hurricane. The concept of dynamical systems has been applied cross-disciplinarily in pure mathematics, and has solved many abstract and previously unsolved problems. This is the most powerful feature of the dynamical systems.

**C: What do you think is the best part of conducting mathematics research?**

L: To me, when there is a problem that I have been grappling with for some time, and suddenly

its solution dawned upon me, that moment of euphoria makes mathematics research very enjoyable. Also, it gives me a great sense of achievement when I see that my work can make an impact on the research direction of peers and younger generation in the field.

B: I once had the honor to chat with Prof. Maryam Mirzakhani, the first female Fields Medalist. She told me that conducting mathematics research is like entering a dark forest where you have no idea of direction. You may only use the tools on hand, and must go through countless failures in order to find an exit. I relish this kind of problem-solving mindset, which attracted me to do

mathematics research.

**C: Besides working on mathematics, what else do you like to do?**

L: Indeed, a professor is also an ordinary person. In addition to my daily research and teaching work, I enjoy watching videos on YouTube and playing video games in my free time.

B: Besides my mathematics research, I have recently been reading some books outside the field of mathematics to broaden my horizon. A while ago, I also became interested in making desserts, especially the more challenging ones. I once tried to make macarons and failed ten times, yet I kept trying. I find this to be quite similar to doing research, because a successful research project is often based on countless failures and even the experiences of others before you, all of which are essential in paving the way to success.

**C: Finally, what would you say to the participants in the HLMA?**

L: It is always better to have a companion when doing research. It is very common for a person to encounter bottlenecks in the thought process. By working as a pair, you can interact and share your views. It is also less likely for two people to throw in the towel altogether.

B: First, choose a good partner to work with so that you would not feel alone and enjoy the research process more. Second, find a good research topic, because the most challenging part of a research is often choosing the topic. Once you have a good topic, you can consider the job half done. Finally, you should muster up your courage and dare to ask questions. No matter if they are undergraduate or doctoral students or professors, they can all give you advice. Of course, you should also do research online and keep yourself updated about the latest developments in mathematics which may inspire you to think of new research ideas.

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