Fostering a new generation of China's mathematical experts

A mathematician said the true ascension of a country in mathematics does not lie in following other countries, but rather in finding a correct direction for itself. It is necessary to recognize China's strengths, and the next three years will see its rise in mathematics.

Speaking of mathematical studies, Shing-Tung Yau is a name that embodies expertise as he is the first Chinese-born mathematician to win the Fields Medal, the highest international award for the subject. He delivered a speech at the Shanghai Master Forum on Science under the theme of the present and future of mathematics in China, which was held in Fudan University on Friday.

"Basic science is diverse, but the foundation of basic science lies in mathematical science and theoretical physics. Mathematics is the foundation of both physics and all engineering theories," Yau said, adding that any strong modernized country must achieve excellence in mathematics.

Looking back at the development of mathematics as a basic science, Yau said ancient China's mathematics level is not inferior to those of ancient civilizations in the world, and its main feature is the emphasis on application.

However, during the mid-Ming Dynasty (1368-1644), the Renaissance in Western countries kicked off the unstoppable development of mathematics, which led to many outstanding mathematicians.

"We in China also have scholars who can match the world's top level. My mentor Shiing-shen Chern can be regarded as one of the greatest mathematicians of the 20th century," Yau said.

In 1946, Chern returned to China and began to cultivate a group of outstanding mathematicians. Later, he went to the United States again and tutored another batch of excellent Chinese mathematicians. In the mid-1980s, Chern become committed to cultivating top-level mathematical talents in China.

"Chern devoted all of his time in his later years into education, with the mission of cultivating China's top mathematicians. This is my teacher's dream and also what we younger generations need to inherit," Yau said.

In 1979, Yau set foot in Beijing for the first time and discovered that China had a long way to go in terms of subject construction and talent cultivation compared to the West.

However, the situation soon improved as China started to send a large number of students abroad and invest more funds in science and technology, which was a farsighted decision in Yau's opinion.

In recent years, many of Yau's students have returned to China and a lot of them are active in domestic mathematical study. He has also established multiple mathematical research institutions in China and organized mathematical competitions with different objectives and evaluation methods.

"Only by connecting with the international community can young scholars break free from mental constraints and follow the forefront of world development to forge their own path," Yau said.

Two years ago, in order to ensure the implementation of the YAU Mathematical Sciences Leaders Program, Tsinghua University's Qiuzhen College was established, with Yau serving as its dean.

His goal is to cultivate a group of top talent in China through this training program. And such talent should be able to lead the world's mathematical development and change the development of basic science.

To achieve this, Yau visited middle schools and even primary schools across the country to select students with outstanding comprehensive capabilities, mathematical potential and expertise as he found that almost all mathematical masters in history began to excel at the age of 13 or so.

To stimulate middle school students' curiosity about mathematical issues, Yau initiated the Shing-Tung Yau High School Science Award. In addition, he launched the Shing-Tung Yau College Student Mathematics Contest, which encourages college students to independently study basic mathematics not narrated in the classrooms or textbooks, aiming to cultivate their true ability to conduct scientific research.

As a related field of applied mathematics, artificial intelligence has recently attracted widespread attention. Yau believes that AI cannot be completed without mathematics, and the mathematics discipline will also usher in new opportunities and challenges in the era of AI.

Challenging the viewpoint that "mathematicians will be replaced by AI", he said that AI cannot replace top mathematicians because the data collected by AI tools are all based on human thinking. Therefore, new breakthroughs cannot be achieved at the current stage.

Yau said that if we want to achieve a real breakthrough in the field of AI, applied mathematicians in China must have a deeper understanding of basic mathematics.

"Only by steadily doing basic research and forging one's own path can we fundamentally solve the 'bottleneck' issues," Yau said.

Yang Aicong, a high school student in the second year of Fudan University affiliated high school, loves mathematics and has won a silver medal in the national middle school mathematics Olympiad.

After listening to Yau's lecture, he said: "Mathematics is a subject that I am very interested in. When choosing my major in university, and in the future, I have made the decision to study combinatorial mathematics."

"As a student of data science, we need to have a clear understanding that the underlying mathematical foundation of data science is modern probability theory and statistics," said Ding Zepeng, a graduate student of the big data college in Fudan University, after listening to the lecture.

He added that facing the current AI trend, students and researchers should not only keep up with research in cutting-edge fields and broaden their horizons, but also settle down to solidify mathematical and theoretical foundations.

The Shanghai Master Forum on Science, based on gathering and disseminating scientific thoughts, was initiated by the Chinese People's Political Consultative Conference Shanghai Committee.

To shape Shanghai into a scientific and technological innovation center with global reach, the forum will generate "Four ONEs" including one journal, one series of books on the frontiers of science, one series of audio-visual media and one science and technology think tank.