Pure Life Of Mathematicians

By Zheng Lei

Recently, I have read some popular science books written by mathematicians. They are not only profound in thought, but also highly proficient in writing. People always think that mathematics is hard to learn, so mathematicians should be like a freak, staring at the empty distance, mumbling some incomprehensible terms (unfortunately, they do most of the time). But this is a big misunderstanding. Mathematics, like Chinese, foreign languages, music and computer programming, is a language tool for thinking and communicating. One can be good at language, music, programming and mathematics at the same time, because these fields are interlinked.

The birth of a theorem

The birth of a theorem is the Autobiography of Cedric vilani, a famous young French mathematician. It is usually difficult for such a young man to have profound experience in writing biographies. The feature of this book is that he and his collaborators (his former doctoral students) have solved a famous mathematical physics problem in three years, and finally won the fields prize, which is known as the "Nobel Prize" in mathematics. This theme itself is very rare, and the author is a person who has broken the public's image of mathematicians: a young man with long hair, a huge cravat and a spider shaped brooch, who loves animation and studies the most profound mathematical and physical phenomena.

This book is not difficult to read. The author takes the diary of key time points in the process of solving Boltzmann's Landau damping problem as the main content of each chapter, interspersed with relevant anecdotes or knowledge introduction of mathematical background, with illustrations and texts, which is convenient for general readers to read. For professional readers, we can learn the key points in the process of solving problems and the moment of inspiration from the email communication between the author and his assistant and some important proofs.

The spiritual world of mathematicians is very pure. Although there are some trivial matters in life, work, or the pursuit of honor, but in general, the mathematician is a simple person. They require very little outside of mathematics, maybe music, maybe very popular literature, to lighten the burden on the brain. This kind of recreation can make him completely free from mathematics for a while, but it doesn't make him continuously distracted. Once the brain is resting, it will work at full capacity and solve mathematical problems efficiently. The problem vilani has overcome is actually the field he studied during his doctorate. It seems to have been solved within three years. In fact, it should be traced back to ten years ago. However, compared with this achievement, this period of time is not long. He is a talented and lucky mathematician. There are many mathematicians who are more gifted than him, but are in a bad situation. For example, Paul erdesh wrote about 1500 mathematical papers in his life. He is one of the founders of probability number theory, but he wears shabby clothes all day. He has no house, family or work. Only his suitcase, notebook and talent accompany him. Gregory Perelman quit his job and spent seven years proving the Poincare conjecture. Some people are too addicted to mathematics and have mental problems. For example, Kurt Godel, the greatest mathematical logician of all time, died of starvation in his later years because of the delusion of persecution. John Nash, who used three theorems to subvert mathematical analysis and geometry in 10 years, was also deeply involved in delusion.

France is a country of mathematics. The author says that Paris has the most mathematicians in the world. There is also a central European country with a weak sense of existence. Hungary is also rich in mathematicians, many of whom are Jewish. Two young Chinese mathematicians are also mentioned in the book, and their mathematical ability is far beyond the international average. In recent years, the state emphasizes the importance of basic subjects. In the Olympic mathematics competition, Chinese students have achieved excellent results. For example, Liu Zhiyu, the champion, was admitted to the Department of mathematics of Peking University, and the competitor he defeated was German Peter Schultz. Liu Zhiyu insisted on leaving home despite the dissuasion of his family and teachers; Schultz became the top mathematics professor at the University of Bonn at the age of 24 and received the fields prize at 31. This is a case worth pondering. Both of them are very talented in mathematics, but the latter is out of interest and love for mathematics, and the former's success in mathematics is more due to intensive mathematics education and training.

This book also shows another aspect of the author's success, which is cooperative research. The role of his assistant, clement, cannot be ignored. Although vilani led the whole research idea and the key idea in the proof, it was difficult to complete it in three years without the help of assistants. Clement's role is to help the author validate his ideas, check the proof process for errors, and make recommendations. It mentions latex, a tool commonly used in mathematical research, which they use to work together and exchange updated research results via email. When the proof is completed, the paper is also completed. Mathematics research is not a "lone wolf" work, the author let us realize the importance of cooperation and cooperation, this process is more exciting than the single task. Mathematics is the only subject in all natural sciences that can make achievements without too many material conditions. What we can do is to cultivate people's interest in mathematics and provide the environment for those with talent.

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