Wu Wenjun's mathematical realm

The British mathematician Hardy said in "A Mathematician's Confession": "Mathematics is a young man's game... I don't know if there are any examples of a man over 50 who has pioneered a major mathematical theory. ”

However, there is such a mathematician in contemporary China. He used his scientific career to give examples that Hardy thought were impossible.

He became famous overseas for his topology research at a young age, and at the age of 38, he was elected as a member (academician) of the Chinese Academy of Sciences, and he shocked the academic community by opening up a new field - mathematical mechanization, and twice won the national high-tech award...

These records of his have not been broken in the Chinese mathematical community today. He is Wu Wenjun, who is known as the "people's scientist.".

In the minds of many people, Wu Wenjun is such a mathematical hero who constantly innovates and has won countless awards, but Wu Wenjun himself said: "Evaluating the scientific development of a country, the height of the group is the real progress!" He longs for "a mathematical realm without heroes"!

In 1977, the 58-year-old Wu Wenjun was already a member of the Chinese Academy of Sciences and the winner of the first prize of the National Natural Science Award, with an impressive title and an honor that is difficult for ordinary people to reach. However, he set off again on the scientific climb with a fighting stance and began a new field that was completely different from the research he had been engaged in in the past—the study of machine proofs of geometric theorems. In the following decades, a mathematical field with strong Chinese characteristics and a strong atmosphere of the times was created--mathematical mechanization.

In 1978, Wu Wenjun officially published his first paper on geometric theorems and their proofs, proposing a new method for machine proofs of geometric theorems. This approach is to algebraize the geometric problems to be proved and have a highly mechanized collation program of algebraic relationships that can be run efficiently directly on the computer. This method is the inheritance of the Cartesian scheme, as the key algorithm of this method - the elimination program of the multivariate nonlinear algebraic system of equations, which is now internationally known as the "Wu method", using this method can not only effectively prove most of the theorems of elementary geometry, but also automatically discover new theorems, and the proof of the main theorems in differential geometry can also be mechanized through this method.

At that time, electronic computers were far from popular in China, and several of the theorems he first tried and succeeded relied on hand calculations, and he humorously called his hands and pens "Wu's computer". The proof process often involves hundreds of polynomials, and any one step that goes wrong will cause subsequent calculations to fail. I can't remember how much, and there is a lot of waste paper alone. Later, the institute had computers, but I had to write the programs myself.

Programming is generally done by young people, in order to ensure that the research process is accurate, for several years, Wu Wenjun has been insisting on programming himself, he learned to write computer programs from scratch, and went to the computer by himself. When the program was programmed on the machine in the late 1970s, the conditions were very simple, and the storage medium was perforated paper bags and punched cards. Such cards were piled up in Wu Wenjun's office with a sack.

Wu Wenjun is the oldest "programmer" in the computer room, and for a considerable period of time, he is also the person who has been on the computer for the longest time at the Institute of Mathematics of the Chinese Academy of Sciences. Often before 8 a.m., you'll see him waiting outside the machine room to open the door. In the computer room, he would work for nearly 10 hours continuously, go home in the evening to eat, and sort out the calculation results. But you'll see him in the computer room two hours later, sometimes working late at night or the early hours of the next morning. The next morning, he appeared in the computer room again to board the machine. 24-hour continuous shaft rotation also occurs from time to time.

At that time, Beijing's Zhongguancun built roads everywhere, dug deep ditches and buried pipes, and Wu Wenjun, who had passed the age of flower armor, often walked home alone in the middle of the night, ditches and bumps, one foot high and one foot low, and sometimes it rained, so he had to wade through the ankleless rain.

Wu Wenjun has a very forward-looking vision for using new tools to help mathematical research. In 1977, he proposed that an immeasurable aspect of the decisive influence on the development of mathematics, for the future development of mathematics, is the impact of computers on mathematics, and in the near future, electronic computers will be as indispensable to mathematicians as microscopes to biologists and telescopes to astronomers.

It was these analyses and judgments that allowed him to make a breakthrough in the process of using computers to prove theorems, thus opening up a new research field in the study of mathematical mechanization.

In the 1980s, Wu Wenjun extended the method of machine proof of geometric theorems to more general equation machine solving, forming a systematic field - mathematical mechanization, and gained widespread application. The method of mathematical mechanization is penetrating into the fields of mechanics, astronomy, physics, chemistry, computer science, etc., and is also being applied to high-tech fields such as robotics, connecting rod design, control technology, and computer-aided design.

The establishment of the theory of mathematical mechanization is completely a new mathematical path opened up by Chinese himself, and the whole process reflects Wu Wenjun's strong spirit of independent innovation. Wu Wenjun often stressed that "we must have our own things, we cannot run with others" and "take our own path" The belief is very firm. "Foreigners have a reason, of course, I will follow, I am not not learning foreign countries, foreign things I have seen, not not not looked, I absorb the part that I feel is correct, can not say how foreigners how to engage in how I have to do." 」

From machine proofs of geometric theorems to mathematical mechanization theories, Wu's research has had a huge international impact. In 1997, Wu Wenjun won the "Herbrand Outstanding Achievement Award for Automatic Reasoning", the highest international award for automatic reasoning; in 2000, Wu Wenjun became the first laureate since the establishment of the country's highest science and technology award for his basic contributions to topology and the creation of the field of mathematical mechanization research; in 2006, Wu Wenjun won the Shaw Prize, known as the "Oriental Nobel Prize". The Shaw Prize Jury wrote in its commentary: "Wu's approach has revolutionized the field and led to a revolution in the approach to research in the field. By introducing profound mathematical ideas, Wu opened up a completely new approach that proved to be extremely effective in solving a large class of problems, not just in the field of elementary geometry. "Its work" reveals the breadth of mathematics. A new example for mathematicians of the future."

In the face of these auras, Wu Wenjun has never had the slightest pride, he said: "I don't want to be a social activist, I am a mathematician, a scientist, my most important job is scientific research." The 'debt' I owe is a scientific 'debt' and a debt to the party and the country. ”

The Party and the people will not forget the heroes who have made outstanding contributions to the country. In 2019, on the 70th anniversary of the founding of the People's Republic of China, Wu Wenjun was awarded the national honorary title of "People's Scientist".

(Author: Li Wenlin and Wei Lei, Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

Source: China Science Daily