Leung Sun Kai

2016 Gold Award

Tsoi Kwok Wing

2010 Gold Award

Cheng Cheuk Hin

2006 GOLD Award

Edward Fan Sin Tsun

2004 Gold Award

Lam Chi Yeung

2008 Silver Award

Lee Yin Tat

2008 Silver Award

Tsoi Yun Pui

2006 Silver Award

Nathan Kung Wai Kwun

2008 Bronze Award

Toby Ng Fung Ming

2008 Bronze Award

Fung Jun Hou

2008 Honorable Mention

Li Fai

2006 Bronze Award

Hui Shun On

2008 Honorable Mention

Li Cheuk Ting

2008 Honorable Mention

Chu Ka Leung

2006 Honorable Mention

Theodore Hui Heung Shan

2006 Honorable Mention

Leung Sun Kai

2016 Gold Award

2016 Gold Award

**Why did you participate in HLMA?**

HLMA is the best platform for secondary students to conduct mathematics research. Through this competition, I hoped that my work could be recognized by the experts.

**What was your secret in writing an impressive HLMA research report?**

A good beginning is half the battle. I put a lot of effort into finding a good research topic. Once I found something interesting, I asked myself related questions to see whether all of these could be turned into a successful research report.

**Is there anything you would like to share with the future participants of HLMA?**

Don’t limit yourself. Keep refining the result you obtained as strong as possible.

**What is your suggestion to make HLMA a better competition for secondary school students in Hong Kong?**

I suggest that HLMA can set the application period a bit earlier so that the students become more aware of the competition, thus spending more time on it.

**Why do you like mathematics? Who inspires you the most?**

The first and foremost reason is the beauty of mathematics. When I was young, I was astonished by the masterpieces of Euler. For instance, Euler’s identity combines the most important constants in analysis, algebra, geometry and number theory. If this is not beautiful, what else is?

**What interests do you pursue when you are not working on mathematics?**

I enjoy playing football. Unlike mathematics, no matter how good you play, teamwork is far more important.

Tsoi Kwok Wing

2010 Gold Award

2010 Gold Award

**How did your experience of HLMA relate to your development?**

Participating in HLMA has crucially changed my perspectives in learning mathematics. When I was conducting the research project, I had several valuable discussions with my team-mate and our teacher advisor and had made significant progress out of these discussions. This made me realize the importance of peer discussions, collaborations in mathematics besides consulting the literature and doing exercises. Having such a mindset motivated me to actively participate in and organize seminars or study groups, consult the professors with mathematical queries and academic advice rather than just turning up in lecture courses when I was an undergraduate.

I was also grateful to have met Professor John H. Coates at the oral defense. Professor Coates subsequently supervised my essay on Iwasawa Theory for CM Elliptic Curves when I read my Master’s degree at the Cambridge University. He had generously shared several of his hand-written lecture notes and his expertise into the subject. It was a wonderful experience for me to not only encounter the beautiful theory originated by Iwasawa, but also to interact with great minds like Professor Coates.

**Do you think overseas universities provides a good environment to study mathematics? Why?**

I read my Bachelor’s degree at the University of Warwick, UK. I hugely benefited from the resourceful environment offered by the Warwick Mathematics Institute (WMI). There are about 100 permanent academics and research fellows in the department. They offer a very wide range of courses at a variety of levels. Besides lecture courses, the department also offers funded research opportunities for undergraduate students during summer vacations. If one is really keen in mathematics, I believe that some overseas universities may offer a resourceful environment which enriches the experience and exposure in his/her studies.

**What is the difference between mathematics students in Hong Kong and overseas?**

In the past few years, I have been working as a teaching assistant for King’s College London. I observed that the students in the UK are very engaged in classes. More specifically, they are very willing to raise their queries whenever they are confused or uncertain about the materials taught. In contrast, students in Hong Kong tend to be spectators in class. I believe such a discrepancy is largely due to the culture of British education which encourages students to participate actively in class.

**What do you think the future of mathematics will be like? Will it focus on application more?**

Certainly a lot of mathematics have found their applications in reality in the last few decades. What is more fascinating to me is that the research in pure mathematics is getting more interdisciplinary in nature.

Indeed, every number theorist would probably agree that there is no way one can do any meaningful research in algebraic number theory with the knowledge of number theory alone. My research interest is in Iwasawa theory which, vaguely speaking, is a tool to describe symmetries of arithmetic objects in terms of values of a relevant complex differentiable zeta functions. While the connection between arithmetic and analysis is itself very interesting, it turns out that such a connection would be much better understood in an appropriate set-up in geometry. Of course it is hard for one to be an expert in everything, so it has become a trend that people from different branches of mathematics would collaborate and come up with exciting ideas. Along with the technological advances, I believe that such collaborations will become more common and will make research progress more effectively than it has ever been.

**Is there anything that you hope to share here?**

The HLMA is a unique research-based competition at high school level. The research projects will be reviewed and commented on by a group of leading mathematicians. I cannot think of any other occasion where one can receive so much constructive advice offered by an intellectual community like the HLMA scientific committee. Therefore I don’t see how one should let such a wonderful opportunity sneak away either. If you are a math-lover at high school, I would strongly encourage you to participate in the HLMA. Not only does it allow you to explore mathematics from a completely different perspective, but also opens you up to a highly intellectual environment. Participating in the HLMA remains one of the most remarkable and memorable experiences of my school days.

Cheng Cheuk Hin

2006 GOLD Award

2006 GOLD Award

**Why did you participate in HLMA?**

I thought of innovative and interesting ideas, but I often had no motivation to investigate them deeply. HLMA acted as a driving force to push me to study my topic systematically and seriously. Through the researching process, I could gain more, no matter in mathematical field, or way of studying or working with partners. HLMA also provides a platform for me to present my findings to the authoritative scholars, I ensured that it would be a valuable experience, so I participated in such a meaningful and challenging competition.

**How did your experience of HLMA relate to your development?**

As I entered the oral defense stage in 2006 HLMA, apart from writing a report, I had the chance to present my findings to the Scientific Committee. I became more confident in my ability of problem solving, analysis and presentation skills. Whenever I come across challenges, I have a belief that I can deal with them.

Also, I understand that it is a good practice, in learning or even in working, to study any problem deeply in order to know the principle behind thoroughly. I would also like to emphasize that, before I won the Gold Award in 2006 individually, I participated in 2004 HLMA in a group of three.

At that time, my group did not enter the final stage, but I still learnt a lot, such as presenting how your daily observation related to mathematics, and team work. The most important thing is that, failure is the mother of success. (I was reminded that unable to win a competition was not a failure. The failure was that our presentation on the study approach and findings were not detailed and systematic enough for the committee to allow us enter the final stage.)

Therefore, do not give up when you fail. Losing a battle does not mean losing the war.

**What is your secret in learning mathematics?**

There are no secrets actually. I wrote my research report by following my train of thought: from my original idea and finding of the topic to the generalized case. I believed that the readers, even not the experts, can understand my report and follow what I have done easily.

My teacher, Mr. Cathay Wong, had more experience on getting touch with research report, he commented on my report in order to make my report meet the standard of research paper. A list of symbols used in the calculations was then added in the early pages for easy reference. Also, he suggested me using “f(.)” instead of using “f()” as the notation representing a function without specifying the variable, which is more commonly used notation.

**Is there anything you would like to share with the future participants of HLMA?**

HLMA provides a platform for participants, not any restrictions. Topics could be widely varied and dabble in different mathematical fields. Students should be creative; they have nothing to lose but everything to gain.

**What were your goals and your views at different stages?**

When I was a secondary school student, my goal was to get good results in public examination, for sure. The reason behind was actually wanting to enter my favourite university and programme. The only mean to achieve this goal was working hard. Having good revision plan was really useful. Luckily, I was qualified to join the Early Admission Scheme, which was a bit out of my expectation. I was then exempted from the A-Level examination, so that I was able to have my Form 6 study without much stress.

In the university, there were so many chances for your development: enjoying hall life (joining the hall sports or culture team, with plenty of practices; playing or studying in mid-night with your hallmates, etc.), which is a characteristic in The University of Hong Kong especially; or experiencing the life of being a committee member of society ( having meetings and campaigns frequently, organizing activities to other students). As influenced by my elder sister, I studied in Canada for an academic year as an exchange student, in order to experience the foreign lifestyle, improve my English as well as broaden my horizon. In short, there were lots of roads in front of you for chosen. You may not enjoy all of the things you have experienced in the university life, but you will never know what you really like without trying. It is a good chance to understand more about yourself in the university.

Coming to the end of tertiary study, getting a good job was my most important task. How to define “good job” may be difficult. The summer job experience may help in answering this question. The chance of having a good job offer would be larger if you know your strengths and weaknesses; and have good preparation on the pre-interview tests and the interview. Now I am a Civil Engineering Graduate in the Government. My goal is to learn whatever I can, and become a chartered civil engineer after the training, so that I can make an impact to the society by my knowledge and power.

**Why do you like mathematics? Who inspires you the most?**

Actually I discovered the mathematical problem before I knew anything about HLMA. “Find a mathematical topic and then study it” was a winter assignment of mathematics tutorial class in my secondary school. This task triggered my interest in observing everything around me. I found it is amazing that mathematics world is so broad and mathematics is everywhere; almost everything can be related to mathematics. I would like to thank Mr. Cathay Wong using this chance, who was my mathematics teacher and the tutor of the mathematics tutorial class in my high school life. He encouraged me to participate in HLMA, which have made a great chance to my life.

**What interests do you pursue when you are not working on mathematics?**

Playing computer games and watching TV are the common interests of teenagers, including me. Also, I have exercise, such as swimming, running or playing soccer, about once a week, because I recognise maintaining a good health is an important thing, and which should be started since when I am still young.

**What do you think the future of mathematics will be like? Will it focus on application more?**

I think the pace of development of applied mathematics is faster than that of pure mathematics (it may be due to the help of powerful computers in twenty-first century), so that we heard about discoveries in applied mathematics more frequently. In my opinion, it does not matter that whether mathematics focusing more on application or theory. The most important thing is more and more people are able to appreciate the beauty of mathematics by admiring the mathematicians’ findings.

**Do you think overseas universities provide a good environment to study mathematics? Why?**

I just took a Statistics course in my exchange programme, so I am not sure about the learning atmosphere in mathematics class; but I can claim that the overseas studying style is encouraging asking question and discussion (even discuss with professor in the class). I believe that this style allows students to exchange their ideas, so that they can learn from each other and learn how to think in different points of view; which is better than spoon-fed style. One more thing I would like to mention is that, I think the pace of learning in overseas is slower than that in Hong Kong (similar case to the pace of life). It is good or not depends on whether you can make good use of your spare time.

**What is the difference between mathematics students in Hong Kong and overseas?**

I am sorry that I do not know too much about overseas mathematics students. However, I can talk about overseas Engineering students. They give me an impression that they are hard working. In general, they are required to take 6 to 7 courses in each semester (I am not sure that this is common in overseas, or just in the university that I studied aboard.), which are a bit more than the requirement in Hong Kong. I always saw the study area and cafeteria were full of Engineering students when I was in Canada.

I observed that the skill of mental calculation of overseas students is generally not as good as that of the students in Hong Kong. People in Hong Kong should keep this advantage, so do not rely too much on calculator or computer.

Edward Fan Sin Tsun

2004 Gold Award

2004 Gold Award

**Why did you participate in HLMA?**

Let me recall… It happened about six years ago, when I was in form 7 and was busy preparing for my A-level exams. I heard from my teachers in high school (from the promotion posters), my parents (from the web) and the professors in CUHK (earlier around that period, I was attending another math program, the EPYMT, organized also by the CUHK math department) that there was a new research-based mathematics competition called HLMA.

As being promoted, this was a serious competition with a strong scientific committee consisting of world-renowned professors. Immediately it drew my interest and I knew that I would have quite a long period of free time after my A-level exam ended. So I decided to participate in HLMA. As some people know, I was originally registered as a group of five persons with my classmates. But as time passed, we had some disagreement on the choice of topics and the attitude towards mathematics. I was being confused for quite a while. At a silent night, I had a long discussion of this issue with my mother. She said, “Son, it is a good chance to show your ability in mathematics, and if you win, it will make your way to become a mathematician much more realistic. Different people have different choices. They (my classmates) treat it as a good extracurricular activity, but it is not yours. You should face it seriously and prove to others that you have the talent in this aspect.”

Her words moved me a lot; I finally resigned from the team and re-registered as a ‘one-man band’.

**How did your experience of HLMA relate to your development?**

The experience of HLMA has many impacts to my development in mathematics, both positive and negative. Undoubtedly, in the course of performing the research, I have learned many techniques in finding references and gathering known results from numerous literatures.

Moreover, this experience is quite different from a problem-solving based competition, one needs to think of the right problem to work on, instead of drilling on a known difficult problem. So it trains up my integrating skills and boosts my creative thinking.

To me, mathematics is a science subject as well as an art subject; you cannot merely use your logical thinking to deal with it. Instead, one needs to use correlative thinking skill to construct new problems to oneself, and then solve it using your logic; experiences on examples as well as intuitions are equally important.

Needless to say, the award itself brought me fame among my fellow schoolmates, and numerous chances supported by the department. But it also brought me some trouble, as old Chinese said, “Huge tree attracts wind,” some students around me were jealous about my privileges and appreciations. Sometimes my schoolmates tried to boycott me or stay away from me. It had been a hard time through my undergraduate study, whenever I have a question (even those which are stupid enough), people’s responds are “You are so brilliant. Don’t trick us, you must know it already.” or “Even you don’t know the answer, we will have no chance to solve it.”, etc. It annoyed me so much, and I knew I have many short comings that I cannot say a word.

However, I think that the experience of HLMA opens my horizon on mathematics, and it worthies much more than its drawbacks.

**What is your secret in learning mathematics?**

There is not much secret, but honestly speaking, there are a few remarks. First of all, the format of writing research papers should be new to all participants. I had spent some time reading papers and books to familiarize the format of stating a theorem, making a definition, and related matters such as citing references, indexing results.

Imitation is the first step to learn, but it is different from copying. You need to digest the way to write mathematics legally, and when you draft your research report, you should not look at the sources even when you are quoting a definition or theorem from that particular book. Since the habit of the usage of language varies from person to person, you will get your original version of the same result each time.

The second point I want to stress is that the terminologies throughout the report must be consistence. Sometimes when we worked for a prolonged period, we would make slight changes to the originally terminology to fit various situations. It is easy to make ambiguity if this change is forgotten or unaware. My way to overcome this problem is to review the older stuff every week, and keep a list of terminologies at hand.

The last remark is that writing a research paper is similar to writing a novel. You cannot write everything by a series of definitions, theorems and proofs. Instead, you need to have an introduction to your paper, elaborations between theorems, and so on, to enrich your report. Remember that the research report is the interesting story you want to share with others, it should not be mixed up with lecture notes used in lessons.

**Is there anything you would like to share with the future participants of HLMA?**

Take this good opportunity to share the fantasy of mathematics. You will learn much faster and much deeper than reading a good book at home or attending a training course. No matter you get an award or not, working alone or working as a team, the most fruitful stuff is experienced during the course of your work.

A small advice to the future participants is that trying to spend more time to find a good topic. A good topic is already halfway to success. Be cautious, a good problem does not stand for a difficult problem; it is determined by its importance in mathematics, its creativity, and its difficulty. If the problem is too easy, it restricts the extent that you can go; if the problem is too hard, you may not have enough time to complete it. A typical good problem is one which allows you stop at different stages, depends on how far you can go.

Lam Chi Yeung

2008 Silver Award

2008 Silver Award

**Why did you participate in HLMA?**

When I was in secondary school, I heard HLMA from my secondary teacher, Mr. Ho. I thought it was a good chance to try to do research on mathematics, so I discussed and finally joined HLMA with my partner.

**How did your experience of HLMA relate to your development?**

HLMA helped me to understand what would be like doing research in mathematics, and gave me confidence about it. It made me feel that I could really do something on mathematics, and it could be one of the reasons why I want to study mathematics further.

**What is your secret to learning mathematics?**

Doing research on mathematics is not easy, normally. But besides thinking hard about the topic by yourselves, in order to achieve more, learning from the others is very important. Especially about mathematics, there are so many great people who had devoted their whole life to doing mathematics, so many brilliant ideas brought to us by our ancestors, and so many clever people working hard on different fields of mathematics.

If you learn more, you would see there are so many connections between different fields of mathematics. In order to have a deep understanding of the topic you are doing research on, you better have a good foundation on different fields. At this stage, you may not be able to understand that much. That is okay, don’t be frustrated. If you are devoted to mathematics, it is just a beginning. But you have to be sincere, learning honestly. You have to achieve your goal step by step. There are no shortcuts.

**Is there anything you would like to share with the future participants of HLMA?**

Besides a better understanding of the topic and a greater exposure to good mathematics, I think a better way to write HLMA research report is to read some mathematics papers to learn their tones and formats. This would make the report look more appropriate. The most important thing is still the content of the report, what I want to point out is only something the competitors may neglect.

**What interests do you pursue when you are not working on mathematics?**

I haven’t thought of majoring in mathematics until I had to choose. At that time, what interested me most are mathematics and computer science. I finally made the decision to major in mathematics, because I thought studying in mathematics was much more challenging and could make me a lot cleverer. I haven’t worried a lot about my future career, since I considered more about what I wanted to do before I considered how I could do it. I just thought “how I could do” is a question that I would eventually find out the answer. Although until now, I still cannot see clearly my future path, what I am doing now is to pursue graduate studies on fields related to mathematics.

I like mathematics simply because I think it is pure and beautiful and it tells me the underlying rules of this world in a simple but precise way. When I was in secondary school, I had many chances to join mathematics competitions. Although I was not outstanding in those competitions, I enjoyed thinking the problems. Also, thanks to my mathematics teacher in secondary school Mr. Ho, who had given me a lot of mathematics materials to read outside the lesson, I had a better exposure to mathematics. I think he is the one who inspires me the most.

**Do you think overseas universities provide a good environment to study mathematics? Why?**

I think some of the overseas universities are good environments to learn mathematics, because they have a larger department of mathematics and gather more cr?me de la cr?me. Even some universities are not as high ranked as those in Hong Kong, seeing how the others in another part of the world learning mathematics is also a good way to have a reflection on the studying style.

Lee Yin Tat

2008 Silver Award

2008 Silver Award

**Why did you participate in HLMA?**

The prize is very attractive and my teacher persuaded me to join it. In addition, I have immense interest and passion in mathematics; therefore, I joined it. At the same time, I read a book called “Information Theory, Inference, and Learning Algorithms”, written by David JC MacKay; it inspired me to take file compression as the topic of my project.

**How did your experience of HLMA relate to your development?**

I became more confident and determinate to further study in mathematics.

**Is there anything you would like to share with the future participants of HLMA?**

Choice of topic is very important. Choosing a good topic in which you are interested in could help you finish the project with satisfaction and happiness. If you choose a very difficult topic, you may not finish it well on account of overwhelming frustration. If you choose a very easy one, your project cannot be impressive and very knowledgeable. Anyway, the most important thing is — never give up! When you started your research and get stuck in the process, just be brave and patient to face the difficulties. Remember “no failure, no success”.

**What is your secret in learning mathematics?**

For secondary school students, self-motivation is very important as you cannot read many mathematics books in school and you have to find it by yourself. For undergraduates, after we know what kinds of academic books are suitable for us, we have to think about our main interest and goal for mathematics.

**What interests do you pursue when you are not working on mathematics?**

I like physics and computer science.

**Do you think overseas universities provide a good environment to study mathematics?**

In overseas, I think we should treasure the chances to know various students from different nations. We have to be active enough to meet them. Also, we have to communicate with those international students and professors. I am sure you will broaden your horizons.

Tsoi Yun Pui

2006 Silver Award

2006 Silver Award

**為什麼你會參與「恒隆數學獎」?**

當我還在就讀中六的時候，有日聽中學老師說起，母校有位高年級的同學在一個叫「恒隆數學獎」的比賽中獨個兒參賽，並獲得了金獎，因此初次認識到這個比賽。後來我從老師口中知道了更多這個比賽的詳情，了解到「恒隆數學獎」是一個以研究為主的數學比賽，與一般的中學數學競賽不同，覺得有趣，因此決定報名參加。

**參加「恒隆數學獎」這經驗怎樣助你發展？**

在恒隆數學獎中的最大得著是拓展了自己的數學視野及加深了自己對數學的興趣。在研究過程中，我參考了頗多的書籍及論文，令我明白到數學的浩瀚和博大精深。無論是閱讀數學家對不同定理的巧妙證明抑或是自己埋頭苦幹思考，對我來說都是樂趣無窮。這些經驗都加深了我對數學的熱愛，令我立志日後在數學方面繼續發展。

**寫作「恒隆數學獎」研究報告時，你有什麼秘訣？**

寫研究報告必須要用心寫，內容最重要，形式則是次要。同學們應該多看參考書及論文，除了可以擴闊視野，在研究的同時學習更多的數學，也可以順道參考論文的一般格式及鋪排，一舉兩得。

**你有什麼想跟未來的參加者分享？**

在比賽中獲得獎項固然開心，但即使落選亦不必難過。恒隆數學獎只是學習數學的一個階段，對數學有興趣並有志在相關方面發展的人應該繼續努力，學習更高深的數學，務求超越自己，更進一步。

Nathan Kung Wai Kwun

2008 Bronze Award

2008 Bronze Award

**Why did you participate in HLMA?**

I love mathematics very much since I was young I enjoy the success of solving a difficult mathematics problem. I had joined a lot of mathematics competitions but HLMA was the most attracting one since it was a research competition which was new and challenging to me. Besides, I learnt that HLMA is one of the most prestigious award organised by Prof. Yau. Thus, I decided to join with my friends.

**How did your experience of HLMA relate to your development?**

HLMA let me understand more about myself and helped me to explore my mathematics potential. It allowed me to gain experience into doing research. It was bitter at first when we had no direction of what to do. But we were extremely excited when we had a breakthrough in the question. I enjoyed this sense of fulfillment very much. This encouraged me to pursue doing research in mathematics or other related fields in the future. It gave me a clearer view of my career path.

**What is your secret in learning mathematics?**

First, we came up an interesting and worth doing topic. Then, we did thorough research in the internet so as to understand deeper in the topic and avoid doing something similar to those had been done in the past. Then persist doing and researching it since it may take a long time to come up with a new idea. By the way, our research problem was actually very famous and had been done by a lot of people. But our report could stand out because we solved the problem in a creative way (in other words, the method was simple but was novel.)

**Is there anything you would like to share with the future participants of HLMA?**

This competition is really exciting. The most important part is coming up with a good problem. This takes a lot of researches and time. Solving the problem is another challenging part as it takes so long to think of a breakthrough idea. The final part is to present it and attend oral defense with prestigious mathematicians. I think it’s not the award itself that counts, but your sense of fulfilment or achievement and the development of interest in mathematics are the most important things that HLMA can give us.

**Why do you like mathematics? Who inspires you the most?**

I like mathematics because I enjoy thinking the questions and the sense of achievement when I successfully find the solution.

**Do you think overseas universities provide a good environment to study mathematics? Why?**

Yes, many foreign countries lay emphasis on science and mathematics. Overseas universities attract many top mathematics talents while many talented students in Hong Kong go to finance and business even they have interest in mathematics as society does not value science or mathematics much.

Toby Ng Fung Ming

2008 Bronze Award

2008 Bronze Award

**Why did you participate in HLMA?**

Indeed, before joining HLMA, I have joined many mathematics competitions. While most of the mathematics competitions focus on students’ competence in calculation, HLMA is the first project-based competition I have ever joined. Meanwhile, I have three friends, who share the same interest with me, gathered to join HLMA.

**What were your goals and your views at different stages?**

In secondary school, we were trained to solve equations in a fast speed and the learning style is examination-oriented. After I entered university, I turned to be much more critical and analytical. I would ask myself why I have to learn this theory and doubt if this theory is correct. I really learn a lot in university with the enlightenment from those professors and the books they recommended.

**How did your experience of HLMA relate to your development?**

By joining HLMA, I gained greater confidence and encouragement. I could clearly see my way which is going ahead for mathematics. In the process of doing our HLMA project, I learnt how to deliver accurate explanation, which benefited for my further study.

**Is there anything you would like to share with the future participants of HLMA?**

Researching immense information is needed; therefore, you can get in–depth understanding for your project. Being active and self-motivated would lead you to a broader path.

**What do you think the future of mathematics will be like? Will it focus on application more?**

I think there are many possibilities for the future development of mathematics. Once, I thought computer science and physics would be the latest trend of mathematics. Recently, after I attended a Newwave talk delivered by Prof. Yau Shing Tung, I thought the application of differential geometry on medical analysis may become a focus in the future. Anyway, analysis on pure mathematics is still essential.

**Is there anything you hope to share?**

I felt delighted to join HLMA which provides chance for youngsters to explore the world of mathematics in a more advanced way. For example, many participants must have learnt how to apply theorems appropriately. HLMA nourished me to build critical thinking. Moreover, I gained the chance to approach different students from different schools. Most of them are very intelligent and I could see different ways of thinking from different students. Besides, since HLMA is like a kind of one-year research project, the whole process seems like planting a flower. When you worked hard on it, your project and you both will become more mature. In addition, HLMA is really worth joining as it did broaden my horizon. When you are still a secondary school student who is passionate in mathematics, it is advantageous to approach university mathematics after your public exams. Then, you will know earlier about university mathematics and the proper learning attitude in university. In short, HLMA is worth joining as you can approach the concept of university mathematics and learn the attitude of doing research.

Fung Jun Hou

2008 Honorable Mention

2008 Honorable Mention

**Why did you participate in HLMA?**

My teacher, Mr. Jonathan Hamilton, encouraged me to join it. Also, I joined it because I thought it was not a lengthy research and I did get interested in it. Meanwhile, the Department of Physical Education encountered a problem about organizing sports teams, which inspired me to make it as my research topic. Moreover, I desired to explore something new.

**How did your experience of HLMA relate to your development?**

In school, problem set, solutions and examinations are what students usually did. But, HLMA provided a precious opportunity for me to learn how to make endeavor to a proper academic research. And I learnt that doing a proper research is not as easy as I used to think. It requires diligence and tolerance. Although I think my HLMA research report is not really useful, my experience enlightened me to devote in more pioneering mathematics research in future. Currently, I have just finished an extended essay in mathematics, “Tautochrones under Non-Euclidean Metrics”. To be frank, my experience of participating HLMA did assist me to finish my extended essay in a better way.

**What is your secret in learning mathematics?**

Choosing a suitable topic is very essential. In retrospect, my HLMA research project should be done in a better way. Also, reading more mathematics books can help us write better mathematical papers. Last but not least, setting aside some time to work on it can guarantee ourselves to get sufficient preparations and amendments.

**Is there anything you would like to share with the future participants of HLMA?**

I think choosing a suitable topic is very important. If you have enough time and get interested in a particularly profound topic, just go ahead. I suggest you to take some more challenges and new things to learn because the spirit of doing research is to explore something new, to discover truths. Besides, joining this competition with peers can avoid from procrastination. For preparations, approaching various mathematical readings would let you know more about mathematics language and then you can write your report more fluently. For example, learning Latex can help you write papers in a more mathematically professional way.

Besides, ideas and points should be well-organized and presented in an understandable way. Eventually, no matter if you can win this competition or not, you should grasp this rare opportunity to interact with professors and other participants. Keeping harmonious and friendly relations with them help you explore mathematics. I am sure you would gain more than what you expect.

Li Fai

2006 Bronze Award

2006 Bronze Award

**Why did you participate in HLMA?**

I was obsessed with learning new mathematics when I was in F.6. HLMA is a project where participants could select nearly any topics they come up in their mind. I decided to take this chance to learn a new topic and explore more on it. This was the motivation for me to join this competition.

**How did your experience of HLMA relate to your development?**

It gave me a taste of what a mini-research is. I felt strongly that mathematics development does not only come from the inspiration of researchers, but more often, it is their perseverance and patience. They may spend several hours, days or even weeks on the same question, to find out the answer, to do algebraic manipulation and logical derivation, and express their conclusion using the language of mathematics. After these processes, I felt satisfied when I understood why mathematicians took those questions into consideration. This experience assured me my interests and ability in mathematics and therefore I chose it as my major in university.

**What is your secret in learning mathematics?**

Every derivation and deduction should be very logical and rigorous. Having a precise and concise conclusion definitely helps.

**Is there anything you would like to share with the future participants of HLMA?**

If you start longing for the endless immensity of the sea of knowledge, you are unlucky and lucky. You are so unlucky that you can never know everything, and anything you have known is probably wrong. But you are so lucky that you are about to discover the beautiful coral under the sea, and it will be the most beautiful thing you have ever seen.

Hui Shun On

2008 Honorable Mention

2008 Honorable Mention

**Why did you participate in HLMA?**

It is because I have an eagerness for mathematics. In the past, I have joined many different mathematics competitions, such as Mathematical Olympiad Competition and Pui Ching Invitational Mathematics Competition. Undoubtedly, these calculation-oriented competitions brought me a lot of advantages.

However, HLMA is the only project-based competition I have ever joined in my life. HLMA is very special that it provided us sufficient time and freedom to choose our topic and develop theorems by ourselves. Without any provision for fixed questions or study areas, we explored our topic actively. If I did not join HLMA, I would not get an in-depth insight for my topic. When I found more questions from my analysis, I discovered that my topic was not only related to geometry but algebra as well.

Moreover, oral defense is the most challenging part throughout the competition. We did numerous preparations and practices for this. We must get acquainted with the knowledge of our topic in order to answer the uneasy questions Scientific Committee would ask. Fortunately, our teacher enlightened us a lot. He triggered us to re-think our questions from another angle. As a consequence, we gained a lot of knowledge and widened our mindsets.

**How did your experience of HLMA relate to your development?**

After joining HLMA, I confirmed that my real interest is mathematics and I determined to study mathematics as my undergraduate major. Also, my experience of joining HLMA increased my criticality and creativity, which help my future academic development.

**What is your secret in learning mathematics?**

Passion. If you have a fondness for mathematics, you will learn it actively and diligently.

**Is there anything you would like to share with the future participants of HLMA?**

Choosing a suitable topic is important. Besides, solving a question from different angles and methods would bring you more questions and enrich your analysis.

**What were your goals and your views at different stages?**

When I was young, I thought mathematics is for fun. After joining HLMA, I confirmed that my real interest is mathematics and I determined to study mathematics as my undergraduate major.

**What interests do you pursue when you are not working on mathematics?**

Apart from mathematics, I like history. Sometimes, I would read some mathematics history and learn some wisdom. For instance, ancient people believed that there were only rational numbers in this world. After many years, some mathematicians discovered other kinds of numbers. This story tells us that some universal truths may not be true. We need to be critical and explore our world from different angles with an open mindset.

Li Cheuk Ting

2008 Honorable Mention

2008 Honorable Mention

**Why did you participate in HLMA?**

With my teacher’s encouragement, I joined the first HLMA competition in 2004, when I was a F.2 student. In that year, my teammates were all senior students, so I learnt a lot from them. Before joining HLMA, I have joined quite many mathematics competitions which required fast calculation speed only. Yet, HLMA is the opposite. HLMA was the first project-oriented and research-like competition I have ever joined. I had to search tons of information by myself and get acquainted with the topic I chose. Therefore, the first time I joined HLMA was very unforgettable.

In 2006, I participated in HLMA for the second time and I was the team leader. To be frank, I was a bit frustrated with my last performance for HLMA, but I just did not want to give up. I wanted to try other things new. So, I chose another topic in which I was interested. As the same as last HLMA, my performance was not awarded. At that moment, I really hoped to know clearly about the shortcomings of my performance.

With an inerasable fondness and enthusiasm for mathematics, I took part in the third HLMA competition in 2008. I was the only member in my group this time. I was passionate in discovering something new in the realm of mathematics. Even though some theorems were discovered by previous mathematicians, I hoped I could develop those theorems in some innovative ways. HLMA provides me a very suitable platform to try different research and mathematical approaches, which cannot be found in other public mathematics competitions.

**As you have participated in HLMA for three times, in your opinion, what kind of uniqueness does HLMA contain?**

As I said, HLMA is a kind of project-oriented competition in Hong Kong, so it drove me to communicate with my teammates frequently and I did learn a lot from them. Also, HLMA provides a valuable opportunity for secondary school students to meet many internationally renowned mathematicians. More delightfully, we could even have dinner and chat with those professional mathematicians after the competition.

Besides, oral defense is a very special and exciting part of the competition. Since those mathematicians would ask us questions face to face, it is quite stressful for us to answer them. However, the whole process of oral defense reminded me the importance of having an in-depth acquaintance with my project.

On the other hand, HLMA provides chance for all participants to publicly view other’s performance during oral defense. I could see different interesting topics created by other participants and I could learn various presentation skills and organization skills from them. Hence, HLMA is a very unique public competition.

**What were your goals and your views at different stages?**

The mathematics taught in secondary school was not very difficult and the goals could be easily accomplished. After I attained certain experiences from HLMA and entered university, I had a clearer picture of how to do a proper research. Thence, in the coming future, I hope I can further study in overseas or do some mathematics research.

**How did your experience of HLMA relate to your development?**

After joining HLMA, I recognized that my thinking method should be more conscientious and serious. The experiences of joining HLMA enriched my proof skills on mathematics. At the same time, I turned to be humbler because those mathematicians and mathematics talents in HLMA broadened my horizons a lot. Besides, my participation in HLMA enhanced my interest towards mathematics.

**Is there anything you would like to share with the future participants of HLMA?**

First of all, no need to choose a very difficult topic. You have to understand that secondary school students have not attained enough foundations for advanced mathematics. Choosing an interesting topic is far more essential. If you can develop some mathematical theorems in some interesting ways, your research may arouse other students’ interests towards mathematics. At the same time, you may doubt the usefulness of your research.

However, just don’t be upset or give up. You have to know that many ancient mathematical theorems were useless long time ago but they become very useful today. So, just go ahead for what you believe. It is still meaningful to try some innovative and creative methods to solve problems. Last but not least, you have to read widely in order to enrich your ideas.

**What is your secret in learning mathematics?**

I think reading widely would help students to explore more about mathematics. Also, thinking about those mathematical theorems helps students improve proof skills and thinking methods.

**What interests do you pursue when you are not working on mathematics?**

I like computer programming which is closely related to mathematics.

Chu Ka Leung

2006 Honorable Mention

2006 Honorable Mention

**為什麼你會參與「恒隆數學獎」?**

我總共參加過兩屆的恒隆數學獎，兩次的原因不盡相同： 二零零四年－即首屆恒隆數學獎的舉行年度，我受當時的隊員陳青璟同學邀請參加比賽。那時主辦機構公佈的種種比賽相關資訊－包括論文、答辯模式的比賽形式，香港、世界知名數學家組成的評審會，恒隆地產對優勝學校、隊伍的支持－都使我等有參加的興趣。而且在陳青璟同學的主導下，我個人對比賽論文成功完成抱有相當的信心，於是在綜合興趣和能力的考慮下我等向領隊陳志強老師提出了參賽建議，並獲老師的信任以組隊參賽。 二零零六年－第二屆恒隆數學獎的舉行年度，在有過一次實在的比賽經驗的支持下，我和另一位有共同志向的隊員黃嘉熹同學決定組隊參賽。那時我等希望可以把手上的一些進行中的探索試以參賽論文的方式完成，使有關嘗試可以更充實地進行之餘，也可傳承更多比賽經驗給同校的後輩。故兩次參賽的心態也不相同。

**參加「恒隆數學獎」這經驗怎樣助你發展？**

參加恒隆數學獎給予我和隊員不少良好的契機，其中不少與我等的個人興趣發展有關係。在完成論文的過程中，隊伍無可避免地要尋找、學習新的數學工具；在準備答辯的過程中，隊伍要考慮報告的重點、順暢而有生氣的表述；這些知識和技巧有不少是能夠在未來個人研究和工作上用到的。隊伍亦須盡量為題目尋找擴充發展的空間，以二零零四年的參賽主題為例，我等雖然未能為橢圓積分尋找更佳的表達式，但卻可試探索高維空間橢球的表現和已有表達式實際應用的評估。這些經驗使我明白進行問題研究雖有時會遇上死胡同，但放開的態度可帶給自己不少額外的得著。

**寫作「恒隆數學獎」研究報告時，你有什麼秘訣？**

進行比賽期間的確有未曾道於人前的瑣事，例如第一次參賽的答辯日，我完全無考慮過用白板、麥克筆以外的物資輔助報告，當時曾經擔心作出報告時不如其他使用幻燈片和電腦的隊伍流暢。第二次參賽、進行答辯前，同校的前輩霍志廣師兄特意抽空幫我等進行綵排，指出報告內容的詳略控制原則和在前輩角度有興趣質問的內容，這使我等準備決賽日時順利不少；而由於研究題目的類型切合，第二次答辯會的報告用片段已經直接使用了報告提及的技術製作，這是一個不錯的實踐方式；2006 年的報告內容只佔手上有興趣的探索的項目開頭的一部分，但編寫時間不足使報告最後兩章要倉促結束。然而，報告製作的過程大體是順暢的，這多得是屆未能參賽的陳青璟同學提供報告排版軟件的使用方法，所以我等私下認為他應也獲一個水晶獎座。

**你有什麼想跟未來的參加者分享？**

不要擔心自己的數學能力不足以參加比賽，用心參賽的話能力自然會跟上。

不要擔心感興趣的東西不似數學研究對象，善用數學工具和作出嘗試就可。

不要擔心答辯時面對評審會的提問會害怕，表示到隊伍的努力就可被認同。

不要擔心參加比賽花費了時間而未能獲獎，把握契機實踐興趣是最大得著。

Theodore Hui Heung Shan

2006 Honorable Mention

2006 Honorable Mention

**Why did you participate in HLMA?**

I participated in HLMA because of my teachers’ recommendation and encouragement. I was already working on an interesting mathematics topic before participated in HLMA so I could explore more about this topic through the whole process of this research-based competition. Also, at that time, I finished public exam, so had a lot of time to work on this research during the whole summer.

**How did your experience of HLMA relate to your development?**

It made me love mathematics even more. After the competition of HLMA, I could confirm to myself that mathematics would become my life-long career. Moreover, I turned to understand more about what mathematicians do (e.g. how to conduct a research), which consolidates my goals in my undergraduate study.

**What is your secret in learning mathematics?**

First, try to be original (this is not a book review!). Second, enjoy the process of doing research. Third, be creative. Fourth, if you join this as a team, distributing duties among yourselves is necessary, but always keep an eye on each other (leave no one working alone!).

**Is there anything you would like to share with the future participants of HLMA?**

Your project should be clear, well-structured, well-organized and written both theoretically and practically. Don’t be shy to consult your teachers or even the professors of CUHK.

**Why do you like mathematics? Who inspires you the most?**

Mathematics is beautiful. When I come across with a question, it is a pleasure to find out the answer, either by reading books or by my own thinking. I feel so good when my curiosity is fulfilled. And sometimes the results are just too beautiful & amazing!

Also, mathematics is very different from other science subjects. First, in other subjects, people first make discoveries out of observations in real life, and then they try to develop theories to explain them.

But mathematics is the other way round: The results are there buried deep, all we do is to explore and unearth. Second, once a mathematics conjecture is proved, it would firmly stand forever, unlike other scientific theories, which can be modified again and again.

**What do you think the future of mathematics will be like? Will it focus on application more?**

It will become more diversified and advanced until it has reached an equilibrium point that people may take their whole lives to learn what mathematics is. In the past, mathematics was developed for real life applications, such as differentiation by Newton. Now, I believe mathematics would continue to be useful with the development of computers.

**Actually I have a commission on mathematics.**

People do generally think that mathematics people are nerds. So my commission is to change this impression, at least starting by myself! Sometimes mathematics is too abstract or difficult that mathematicians can rarely share the joy or beauty of mathematics with everyone in the world. So I hope I can share the beauty of mathematics with as many people as possible. Thus, I am thinking of making an online teaching/sharing on YouTube, then anyone can access to mathematics easily and conveniently!