·Mathematics has no distinction between old and new, Chinese and foreign, useful and useless. We must allow everyone to enjoy the wonders of mathematics, and the notion that mathematics is only for the gifted must change.

·The development concept of big mathematics requires mathematics not to stick to its own discipline, but to be good at using other auxiliary tools. A prominent manifestation of the development of artificial intelligence in the field of mathematics is machine proof.

What is the development concept of big mathematics?

On March 14th, the International Mathematics Day in 2023, Zhang Jiping, academician of the Chinese Academy of Sciences and professor of liberal arts at Peking University, was invited by the Chinese Mathematical Society, the Chinese Society for Industrial and Applied Mathematics, and the Chinese Operational Research Society to publish a speech on the topic of "The Development View of Big Mathematics" speech.

Academician Zhang Jiping WeChat public account @Peking University School of Mathematical Sciences data map

Zhang Jiping used the words of Mr. Wang Guowei, a master of Chinese studies, that "academics have no distinction between new and old, no distinction between Chinese and foreign, and no distinction between useful and useless". There is no distinction between old and new, Chinese and foreign, and no distinction between useful and useless in mathematics.

He also quoted Efim Zelmanov, a master of mathematics and a winner of the Fields Medal, as saying that mathematics is truly international and global, there is no American, French or Chinese mathematics, there is only one world. In mathematics, people from different countries study the same problem, come to the same conclusion, and learn from each other together.

Zhang Jiping said that we are now in an era of great change. The great era requires great mathematics, and great mathematics requires a great outlook on the development of mathematics. Artificial intelligence, machine learning and other technologies will make the development of mathematics faster, and new things will appear more and more complex. Because of this, mathematics needs to move toward comprehensive unity at a new depth and height, which is the development trend of big mathematics. Only in this way can we have more theoretical and applied results.

According to information on the official website of the Department of Mathematics, School of Mathematical Sciences, Peking University, Zhang Jiping was born in July 1958 in Chengwu County, Shandong Province. In January 1978, he entered the Department of Mathematics of Shandong University to study. In 1987, he received a Ph.D. in Basic Mathematics from the Department of Mathematics of Peking University, and stayed on to teach there. In 2019, Zhang Jiping was named an academician of the Chinese Academy of Sciences. Zhang Jiping served as the vice chairman of the Chinese Mathematical Society, a member of the Development and Exchange Committee of the International Union of Mathematicians, the executive deputy director of the Department of Mathematics and Physics of the Science and Technology Committee of the Ministry of Education, and the vice chairman of the China Youth Science and Technology Association.

According to the official website of Southern University of Science and Technology, Zhang Jiping also serves as the executive director of Shenzhen International Mathematical Center. "He has made outstanding achievements in the research of finite group representation theory, especially his work on solving two major problems of group theory master Brauer has become an important basis for the theory of self-defense promotion of high-dimensional Galois representations."

math for everyone

Zhang Jiping said that in history, mathematics has never had such a direct and profound impact on our lives as it does today. The theme of this year's International Mathematics Day is "Mathematics for Everyone", which means that mathematics is for everyone, because we all have different levels of mathematical ability, and we must let everyone enjoy mathematics Amazingly, the notion that mathematics is only for the gifted (engaged) must change.

In this regard, he gave an example: 185 years ago, there was a teenage mathematical genius named Galois in France who created finite fields, but he was killed at the age of 21 because of jealousy. , finite fields have no practical use other than purely mathematical interest. However, finite fields are the basis of cryptography and coding. Today's financial and financial transactions all over the world are processed based on finite fields. The same is true for mobile phones, and we use mobile phones to make calls, use WeChat to pay fees, etc. etc., are all based on this theory of finite fields.

"Professor Xing Chaoping from Shanghai Jiaotong University recently solved the eighth problem of Huawei. Then the so-called eighth problem is the problem of algebraic coding. The problem of algebraic coding is to study arithmetic algebraic geometry on finite fields." Zhang Jiping said.

2021 Huawei's Eighth Question - Seminar on Algebraic Geometry Code.

According to the official website of the Germanov Mathematics Center of Southern University of Science and Technology, from April 26 to April 28, 2021, the "Huawei Eighth Problem-Algebraic Geometry Code Seminar" hosted by the center was successfully held. The seminar was jointly organized by academician Zhang Jiping, executive director of Germanov Mathematics Center of Southern University of Science and Technology, Zhang Gong, chief scientist of Huawei Academia Sinica Theoretical Research Department, and Xing Chaoping, professor of Shanghai Jiaotong University.

A netizen raised a question in the communication session: Mathematics is too abstract for the general public, so how can we make mathematics understandable to everyone?

Academician Zhang replied that there are actually too many examples of the application of mathematics in daily life. From these aspects, mathematics becomes a natural thing. "You don't need to understand its theorems and theories, you don't need to do (mathematics), you just need to understand it."

Artificial intelligence helps mathematics research, and we look forward to the emergence of more "condensed matter mathematics" big mathematics

Zhang Jiping said that we are in the information age, and the information revolution is rooted in mathematics. In a sense, the information revolution will surpass the huge impact of the agricultural revolution and industrial revolution in the history of human civilization. In the past, it was to enhance human physical strength, but now it is trying to enhance brain power, and in the context of the artificial intelligence industrial revolution, make machines work and learn.

Zhang Jiping said that the development concept of big mathematics requires mathematics not to stick to its own discipline, but to be good at using other auxiliary tools. A prominent manifestation of the development of artificial intelligence in the field of mathematics is machine proof. Machine proof is the realization of theorem proof through computer and auxiliary proof tools.

Zhang Jiping said in the lecture that Magma is a powerful algebraic calculation package developed by the Computational Algebra Group of the University of Sydney. "I've been paying for it.

He said that with the further development of artificial intelligence, machines have a certain ability to choose and judge, and more mathematical theorems proved by machines can be expected to appear. "The development of mathematics (in) theory is becoming more and more profound, more and more abstract, and more and more differentiated. At the same time, there is also a trend towards comprehensive unity at a new depth and height."

For example, Zhang Jiping said, "Higher-order categories can be used to describe quantum field theory and quantum entanglement." "Condensed matter mathematics tries to unify different fields of mathematics, including topological geometry and number theory."

"In fact, one purpose of condensed matter mathematics is to provide everyone with a convenient framework to deal with algebraic objects with topological structures. Another purpose is to turn algorithm analysis into commutative algebra and analytic geometry into algebraic geometry." Zhang Jiping Said, "We believe and look forward to the emergence of more 'condensed matter mathematics' big mathematics. Big mathematics requires great cooperation and exchanges among mathematicians."

In addition, Zhang Jiping said that the world view of mathematics is helpful to the development of data science. For example, how to abstract the commonality of some things from the vast ocean of data for research. Mathematical methods of induction, reasoning, etc. can all play a very good role in data science.