At the first Macao Science and Technology Awards Ceremony held on 19 October 2012, the University of Macau (UM) won nine prizes across three categories as well as the Postgraduate Science and Technology Research and Development Awards by nineteen postgraduate students, eclipsing all other higher education institutions in Macao. Prof. Qian Tao’s project, Time-Frequency Analysis of Transient Signals and Algorithm: Harmonic and Clifford Analysis of Signals, won the sole first prize in the Natural Science Award category, representing yet another recognition of his impressive academic achievements. Even more impressive is Prof. Qian Tao’s life story, which he will share with us in this article.
Stay Hungry, Stay Passionate
Born into a well-educated family, Qian Tao has been fascinated with maths ever since he was a child. His gift for maths became more apparent after he began secondary school. He was recommended for direct admission to the famous Beijing No. 4 Middle School after winning the first prize at a major maths competition. Even in the more-than-a-century-old school with the best students from Beijing, Qian Tao quickly stood out from the rest. In the first year he was appointed assistant to the geometry teacher, and in the second year he was elected assistant to the homeroom teacher in study-related matters. Towards the end of his second year at Beijing No. 4 Middle School, the political climate in China changed abruptly — the dark cloud of the Cultural Revolution spread over the whole country, and Qian Tao was soon classified into the group in need of “re-education” due to his family background. With the “Down to the Countryside” movement sweeping across the country in 1968, Qian Tao was sent to a village in Shanxi province, where he spent nine difficult years.
Being banished to the remote countryside didn’t diminish Qian Tao’s passion for maths one bit. Not only did he continue to teach himself, he also co-founded, on 20 July 1969, a modern secondary school maths study group with four other like-minded young men. This group deliberately kept a low profile during those turbulent years and remained obscure to almost everyone except a handful of senior mathematicians in Beijing, who gave the group the nickname “The Quintet”. After a story about their experiences was published in 2001, The Quintet quickly became the object of extensive media coverage both at home and abroad.
Members of The Quintet were scattered far and wide and mostly kept in touch through correspondence. Occasionally when they returned to Beijing they would consult with their teacher Han Nianguo, a mathematician, about maths problems, but most of the time they learned on their own. For a long time, after finishing each day’s work, Qian Tao followed his daily routine of studying maths deep into the night by a dim oil lamp, and each morning his nose would be black from the oil. He still remembers how he worked through the Boris Pavlovich Demidovich Exercise Book of Mathematical Analysis Problems, one problem at a time. “That exercise book was from the Soviet Union, and it contained over 4,500 problems, which were very difficult,” recalls Qian Tao. “Each morning before I left far farm work I would copy ten problems onto a piece of paper, and then I would try to figure out how to solve them while working, and I would write down my solutions after I returned home.” Bit by bit, he taught himself the fundamentals of university-level maths, and also learned English. “During the first month, I studied the English textbook for form-1 students, one lesson a day,” says Qian Tao. “I tried to memorise the new words and pronunciations. In the second month, I picked a maths book written in English that I wanted to read, and I started from the introduction, one sentence at a time, until I understood the words and grammar. In the third month, I was already reading the whole book.”
During the nine years in the countryside, Qian Tao tilled the land, grew vegetables, tended sheep, and even worked as a barefoot doctor and a worker of a drilling crew, but he never stopped learning maths. In the late 1970s, the first streaks of light broke across the dark political landscape of China. In August 1977, the reinstated Deng Xiaoping mentioned in an important speech the government’s plan to “resume national college entrance examination”. The news shone a welcome ray of hope into nearly a decade of suffering endured by The Quintet. Their teacher Han Nianguo encouraged them to apply directly for postgraduate studies. He told them, “The resumption of the college entrance exam and postgraduate admission is exactly for people like you.” In December of the same year, the five were all accepted to universities. Less than six months into his new life at Shanxi University, Qian Tao dropped a bomb by expressing to his department his intention to apply to be a master’s student at Peking University. The management of Shanxi University thought this young man was too conceited — how could a secondary school graduate, who had stayed in the countryside for nearly ten years, even begin to entertain the idea of skipping undergraduate studies and going straight to the most prestigious university for postgraduate studies? Finally, Shanxi University grudgingly arranged an extremely strict qualification test in two subjects, English and Advanced Algebra, invigilated by two teachers. To everyone’s amazement, Qian Tao effortlessly scored 98 points on a 100-point scale, and he was the talk of the town when he became the first person from Shanxi province to be accepted by the Department of Mathematics at Peking University as a postgraduate student.
“You Must Have Vision and Think For Yourself”
Looking back, Qian Tao says those difficult years in the countryside have had a profound impact on him. “Of course entering Peking University was significant, but those years were just as significant in terms of forcing me to exercise my will and helping me to develop the habit of self-education, which continued to serve me well in my later studies and work,” explains Qian Tao. “I will never stop and think that I’ve already arrived, and I always stay hungry for knowledge, and passionate about new stuff, and this is because of my experiences in those years.” Being persistent is much easier said than done, especially in that turbulent period. How did Qian Tao manage to find the courage and motivation to keep going and never give up when the future seemed completely dark? “My source of motivation was really just my independent thinking about the future trends of society,” remarks Qian Tao. “I used to read works by great philosophers like Hegel, Russell and Kant, and I just felt it the Cultural Revolution wasn’t right. They told me that maths, or knowledge as a whole, was not necessary? That was against the laws governing the development of society! I mean, how can you imagine a country developing technology and industry without its people possessing foundational knowledge? That’s just impossible! I don’t blindly believe what I’m told. You must have vision. You must look at the world with your own eyes, and think for yourself. And that’s why I never gave up studying even in those years.”
At Peking University, Qian Tao studied under the renowned mathematician Cheng Minde, specialising in harmonic analysis in Euclidean spaces. By the time he received his PhD degree from Peking University in 1984, he had already achieved some impressive results together with his teachers Cheng Minde and Deng Donggao. His nine papers were published in top academic journals in China including Science China and Acta Mathematica Sinica. He was among the first recipients of the National Science Progress Award. Later he went to work at the Institute of Systems Science, Chinese Academy of Sciences. It didn’t take long before his outstanding research caught the attention of academic institutes overseas. In 1986, he was appointed postdoctoral research fellow by the Australian Academy of Science and went to Australia to carry out research on pure maths. He began teaching at the University of New England in 1992. In 2000 he joined UM, continuing with his teaching and research.
“For a Maths Lover, the World Is Mathematical”
“Different people look at the world differently,” observes Qian Tao. “For example, Mozart could compose a piece of music after a walk in the garden, because to him the world was musical. A painter sees a pictorial world. Likewise, for a lover of maths, the world is mathematical.” Qian Tao sees maths everywhere, and he didn’t miss a beat when asked to give an example. “Let’s say you need to go through immigration clearance, and you need to decide which queue to join, then you should pay attention not just to the length of the queue, but also the speed, as well as whether the officer is a male or female, because female officers tend to be faster,” explains Qian Tao. “This actually has something to do with derivative and difference.”
When Qian Tao joined UM in 2000, there was no PhD graduate from the Department of Mathematics. Around 2001 and 2002, Qian Tao had his first PhD student at UM, Kou Kit Ian, who was also the first doctor of maths to graduate from UM. Qian Tao has a unique philosophy about educating student. “I don’t require my students to write many papers,” he says. “I encourage them to be creative, to do something original. Of course they can start by picking up the crumbs left behind by masters, and there is a good chance that doing so could lead them to academic recognition or even published works, but eventually it’s creativity that really matters.”
Qian Tao believes that despite its small size, Macao is on a par with mainland China in terms of education quality, and perhaps it is even blessed with a unique advantage mainland China doesn’t have. “Macao is located between mainland China and the West, and the academic atmosphere of UM is quite good, with many international exchange opportunities,” comments Qian Tao. “Students who have finished their studies here would find it easier to pursue further education abroad.” In 1986 Qian Tao began to actively participate in international academic exchange activities. He has been to a dozen or so countries where he conducted research and published a large number of academic papers in collaboration with mathematicians from around the world. He has been invited to speak at numerous important international conferences. He credits his being able to constantly break new ground in his academic research to the help and guidance of his teachers, including Prof. Cheng Minde from Peking University, a former member of the Chinese Academy of Sciences, and Prof. Alan McIntosh from Australia, fellow of the Australian Academy of Science. “It’s important for students to have good teachers or mentors to guide them, until they are academically mature enough to produce their own fruits.”
In recent years, UM has launched a series of reform measures, with the goal of becoming a world-class with regional characteristics and equal emphasis on teaching and research, a university that produces outstanding graduates through an international-standard mode of operation, excellent teaching and innovative research. As one of the foundational subjects, maths naturally has been identified as a key object of reform. “Since he took office as the rector, Prof. Wei Zhao has spared no effort to develop our department,” remarks Qian Tao. “He broke through the misconception that Macao doesn’t need an undergraduate programme in maths, and supported the launch of an undergraduate programme in maths. Also we search internationally for outstanding professors through a very strict selection process. Usually we would select only a few out of several hundred applicants. So I sincerely believe UM’s faculty will become stronger and stronger.”
With four master’s students, six PhD students and three postdoctoral students to supervise, two courses to teach, and probably two more new students to take under his wing next year, Qian Tao expects the coming days to be even busier. But he knows he will enjoy every minute. “Young people must have interests and direction, and once they decide what they want to do with their life, they should go for it and not give up easily. As teachers, we should encourage our students to pursue their goals,” says Qian Tao.
Prof. Qian Tao
Graduated from Peking University, has worked at the Institute of Systems Science, Chinese Academy of Sciences; Macquarie University, Flinders University and the University of New England, Australia. Currently he works in the Department of Mathematics, Faculty of Science and Technology, University of Macau. He has been involved in the organisation of numerous international conferences, and has published over 130 conference proceedings, papers, books and book chapters.
Prof. Qian Tao’s Prize-winning Project, “Time-Frequency Analysis of Transient Signals and Algorithm: Harmonic and Clifford Analysis of Signals”
The Assessment Committee rated Prof. Qian Tao’s project as having the significance of “new discoveries”. Five well-known experts unanimously considered it to be exceedingly outstanding, with marked progress and impressive achievements in theoretical research. What is this research about?
Expressing Complex Things in Simple Ways
“According to the oldest classification method, maths can be roughly divided into three areas — analysis, algebra and geometry, and my research belongs to the first category,” explains Qian Tao. “It’s actually a further development on calculs. What a function does in layman’s terms, is to change figure A into figure B, and the core problem is how to express a complex fuction in some simple, more workable ways, which is in effect a process of conversion or division. And my research has to do with this.”
In his research, Prof. Qian challenged the classic Fourier theory. “We took his interpretation, scope and expression one step further,” explains Prof. Qian. “The classic Fourier theory is like a one-sized school uniform for students of different heights and sizes. Ours is more like a tailor-made suit. We tried to express complex things in simple ways, so we could achieve approximately the same effect faster. For example, if I need to transmit a signal, and if I could use fewer parameters to express a complex function, that would mean less time in transmitting.” It is not hard to imagine the enormous potential of this research in terms of practical applications in maths, engineering, data and signal analysis and processing technology, especially given the rapid advancement of digital technologies.
No Finish Line in Scholarly Pursuit
Prof. Qian discloses that his next focus will be on the application of Adaptive Fourier Decomposition in maths and engineering technology, and in the meantime will continue with his research in a more in-depth manner. For him, there is apparently no finish line in scholarly pursuit.
In his speech at the first Macao Science and Technology Awards Ceremony on behalf of all the other prize recipients, Qian Tao thanked the Assessment Committee for its recognition of the invention, and thanked UM’s Research Committee, especially UM Rector Prof. Wei Zhao and Vice Rector Prof. Rui Martins, for their great support. He regrets that due to time limitations, he was not able to include in his speech the names of the following people to whom he also owes a debt of gratitude. They areLi Luoqing, Chen Qiuhui, Li Hong, Xu Yuesheng, Zhang Haizhang, Wang Rui,Yan Dunyan, Yan Lixin, Li Dengfeng, Zhang Liming, Tan Lihui, Wang Yanbo, Dang Pei, Mi Wen, Li Shuang, Ho Io Tang, Leong Ian Tak, Kou Kit Ian, Li Zhixiong, Mai Weixiong, Michael Steesin, Elias Wegert, and Wolfgang Sproessig.
Macao is a small city with big potential. Some members on the Assessment Committee commented that among the four territories of Macao, Hong Kong, Taiwan and mainland China, Macao has made visible progress in science and technology development. Lau Si Io, secretary for transport and public works of Macao SAR, also stressed at the award ceremony that the SAR government will increase resources in scientific research and science popularisation in order to provide a bigger stage for scientists and engineers to demonstrate their talent. There is every reason to believe that with the support of the SAR government and the dedication of outstanding scientists like Prof. Qian Tao, Macao’s science, technology and education will have a bright future.
Macao Science and Technology Awards
In 2011 the Macao SAR government promulgated the “Regulations of Science and Technology Awards” which states the launch of Science and Technology Awards, Postgraduate Science and Technology Research and Development Awards, and Special Rewards. The Science and Technology Awards are divided into three categories: Natural Science Award, Technological Invention Award and Science Technology Progress Award. The purpose is to reward individuals and organizations who make significant contributions to science and technology in Macao, thereby motivating local scientists to be dedicated and creative in order to accelerate the development of science and technology in Macao.
