Paul Halmos gave an account of his over-50-year career as a mathematician in his automathography I want to be a mathematician. I aspire his grit, pure passion for mathematics, his far-reaching influence over the subject. I, too, want to be a mathematician. But there is a long road in front of me; it is protracted, tantalizing, and obscure. I can see neither the view to come nor where it eventually leads me. Fortunately, however, looking backwards I see how the journey, which was made up of a few upfront battles with hardcore math theories and constant interactions with formulae and equations in study, has brought me where I am now.
I had absolutely no clue what I was passionate about at the turning point between high school and college. Entering the college meant that twelve years of stiff, dogmatic, bound-by-textbook learning period was over and an abrupt air of freedom was granted. On a daily basis, I passed through several lectures on different subjects with no emotion towards the chalk marks or the lengthy proofs in textbooks, killing the free time after lectures with films and books. I was baffled by the vast variety of subjects in the syllabus. I was confused about the way I was to spend the four-year college life. A turning point for me was the first mid-term test of Mathematical Analysis I, where I solved every problem correctly and had a perfect score. The professor of this lecture happily congratulated and praised me, and for the first time since I ever entered college, I had a sense of fulfillment. As a candle was lightened in the middle of darkness, I thought to myself, I might have a talent for math. I became determined to study from that point, not only analysis and algebra, but all the subjects offered in the department. Till this day I am grateful to this professor for his generous and genuine encouragement to a puzzled freshman.
I pursued my undergrad and graduate study in an engineering field. Endless formulae and equations were required to be recited and applied correctly, in most cases without the need to recognize the mathematical derivations behind. I could write functioning computer programs, conduct valid lab experiments, and score high in almost every course. I believe that math was a hiding aid and guidance behind my learning process. Using the math tools to digest those engineering formulae helped me grasp the knowledge quickly and provided me with a distinct perspective in understanding the obscure theories. I remember that after my first publication, which was a short conference paper on the topic of unsupervised machine learning, my supervisor at that time encouraged me to consider an academic path because his impression was that I was “very good at mathematics”. I understood that this “very good” was only in comparison to engineering researchers—my math skills were negligible to any mathematician by training—but I was aware as well that solid and strong background in math is bound to be a pillar throughout a research career.
Time soon came that I must choose a research focus for the PhD project. I decided to join a lab at ETH and work on developing a mathematical theory behind deep learning. Partly because I expected to obtain intensive mathematical training and make up for what I missed not having a degree in math, i.e., I wanted to be a mathematician. Most of the days in this PhD program I am truly enjoying my work, and I consider this a sign that I made a good choice.