It is a rare honor for me to receive this honorary degree from the great University of Waterloo. I am particularly grateful because in my research area -- discrete mathematics -- the University of Waterloo has the strongest faculty in the world. Indeed I am humbled to be selected to speak to you today.
First, let me say congratulations! You have achieved a milestone and are about to start a new phase of your life. At this new beginning, I am delighted to have this opportunity to offer a few words of advice and share some of my stories.
I grew up in Kaohsiung, a southern city in Taiwan. Taiwan rhymes with Taiphoon because the island has frequent visits of hurricanes. I was lucky to enjoy peace and prosperity during my growing up years while this was not the case for my parents and their parents. After high school when I faced the choice of majors, my father gave me his advice, "Mathematics is the foundation of science. If you are good at math, you can do anything. You can easily switch to other areas later if needed."
His words still ring true. At my first job at the Math Center of Bell Labs, my research in graph theory easily branched out to computer science and communications. Over the years, I worked on various graph problems, some of which are connected to the pure side, such as number theory, spectral geometry. Some graph problems are connected to the applied side such as optimization, computation, physics and chemistry. In recent years many interesting problems arise in the analysis of information networks and search algorithms. Although the topics might sound different, the mathematics underneath are just the same. It turns out that I never need to switch to other areas after all.
One phrase that we often hear is "to do what you love, and love what you do". There are many good reasons behind this saying. The more you love what you do, the more likely you will do it well. If your work is like play, you will wake up in the morning happily looking forward to playing. You have a long career of many, many happy years in front of you. After saying this, let us face the fact. In this world of reality, not everyone is doing what they love. How do we increase the chance to be among the few to be able to do what we love to do?
A somewhat surprising answer that I am about to give you is "to be lucky". I have met some people who seem to be very lucky. In fact some of them seem to be always lucky. So I try to analyze why some people are luckier than others. Here is what I can report.
- Luck is for the prepared.
A somewhat different quote by the philosopher Seneca stated, "Luck is a matter of
preparation meeting opportunity." On the surface, luck seems to be closer to opportunity than
to preparation. I would like to argue the other way around. In probability theory, any
rare event (like finding your dream guy/girl) usually happens with some low probability p
for each instance of meeting a new friend. However, the probability of success is almost 1
since the probability of failing is (1 - p)^n which approaches zero as n goes to infinity. Thus,
over a period of time among multiple tries, almost surely opportunity will arise. So, the
key is to be ready so that you can catch the opportunity when it comes your way.
With your new degree in hand, you are basically prepared. Still, I will share with you a story about my husband, Ron Graham who is an alumnus of Waterloo since he received an honorary degree here in 2010. Ron gives beautiful talks with great ease and a natural eloquence. It looks so easily done but only I know that he sometimes spent hours and hours on one single slide. There is some truth in the saying "Preparation makes perfect".
- Another fact that I found helpful is that you need friends. Peer review means you are evaluated by your peers who hopefully are among your professional friends. You need friends in your life and you need friends in your profession. In particular, your college friends are likely both in your life and in your profession. When I went to college at National Taiwan University, in my year there were a relatively large number of women in the male-dominated math department. At the start of the freshman year, it was intimidating since some of the men seemed to know all the mathematical terms that we had no idea about. However we stuck together and worked on problems together. At the end of four years, it turned out the top students were all women. In mathematics, as long as you know your theorem, it does not matter if you are short or are a women. We went to grad school in the US and struggled through the ranks . We live in different cities now but our friendship continues and we see each other regularly at math meetings. People started to notice that four women mathematicians -- Alice Chang of Princeton University, Winnie Li at Penn State, Gloria Wu at U of Illinois and myself are all from the same undergraduate class. Professor Chern of Berkeley wrote a popular article calling us "Four golden flowers in math". MAA made a poster about women mathematicians which included four of us there. It is very true that your college friends are your friends for life. Having said this, I also believe that it is important to keep making new friends. At this information age, friends and collaborators are a major source of information who you can learn much from.
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Lastly, I'd like to add one most important piece of advice --- "to be curious and stay
curious". Curiosity leads to new paths, new directions and new adventures. If there
are two paths in front of you, it is not necessary to pick the one that is familiar. Robert
Frost said, "Two roads diverges in a wood and I took the one less traveled by, and that has
made all the difference". Stay curious and let your life be filled with wonder.
Thank you very much and good luck.