Mr. Yang Zhenning had a significant impact on mathematics in the field of modern physics, which was particularly significant in the second half of the 20th century. His contributions to the field of mathematics are comparable to those of Witten, and behind them are many world-renowned achievements and intricate academic relationships.

Yang Mills theory is an extremely important achievement of Chen Ning Yang.

When he gave a lecture on Yang-Mills theory at Princeton, Pauli and others in the audience raised questions about the mass of non-Abelian gauge bosons. This scene reflected that the theory was under strict scrutiny at that time.

Not long after the theory came out, in the late 1970s, Singer recommended the Wu-Yang dictionary to the mathematical community, which inspired mathematicians' enthusiasm for studying Yang-Mills theory.

In 1987, Hitchin defined the Higgs bundle on a one-dimensional complex manifold and studied the Yang-Mills equation on it. This achievement can be regarded as a major progress in the field of Yang-Mills theory.

In the process of mutual promotion between mathematics and physics, Yang-Mills theory still plays a key role in the field of low-dimensional topology.

Jones revealed a new knot invariant, the Jones polynomial, in 1984, which is closely tied to the theory.

The research scope of this theory has been extended to the branch of mathematics known as low-dimensional topology. This expansion highlights the value of the theory and also demonstrates the far-reaching impact of Yang Zhenning's contributions in this field.

Chen Ning Yang also made another contribution in the field of mathematics, which is the famous Yang-Baxter equation. This work had a significant and lasting impact on the field of mathematics.

In the late 1970s, the Soviet school of mathematical physics led by Fadeev named this equation the Yang-Baxter equation and conducted in-depth research on its application in the fields of mathematics and physics.

This equation is an important bridge between physics and mathematics, showing Chen Ning Yang's significant influence in both subject areas. Through his achievements in the field of physics, he promoted the advancement and in-depth study of mathematics.

The research and application of the Yang-Baxter equation have expanded to many fields, and many mathematicians have used it as a starting point to conduct new explorations or gain inspiration from it.

This reflects Chen Ning Yang’s continued contribution to work in the field of mathematics, and his equations continue to provide nourishment for subsequent academic research.

In the second half of the 20th century, Witten's influence on mathematics could be compared with that of Chen Ning Yang.

Witten's theory was deepened by Rechtihin and Tulayev, forming a rigorous mathematical system. This system can construct invariants of three-dimensional manifolds. In addition, Witten also used Yang-Mills theory to explain the Hovanov homology theory, which attracted the attention of many mathematicians.

Although Witten's achievements in the field of mathematics are comparable to that of Mr. Chen Ning Yang, their respective research methods and growth backgrounds are still different.

The two advanced mathematical theories closely linked to physics in their respective fields, promoted dialogue and interdisciplinary progress between mathematics and physics from multiple perspectives, and jointly created an academic environment in that era in which physics had a very close influence on mathematics.

Two papers on statistical mechanics published by Li Zhengdao and Yang Zhenning in 1952 each have significant academic value.

In their research, they came to the conclusion that the zero points of a certain type of partition function are all within the unit circle. This conclusion, the Lie-Young unit circle theorem, has been widely recognized.

Although this work is quite critical in the field of statistical mechanics, it is slightly inferior to the impact of Yang-Mills theory and Yang-Baxter equation on the mathematical world.

The connection between statistical mechanics and mathematics is one of the local manifestations of the impact of physics on the progress of mathematics.

The Li-Young unit circle theorem occupies an important position in the field of statistical mechanics. This achievement cannot be underestimated.

The varying influence of multiple achievements during the same period highlights the significant contribution of Yang-Mills theory and Yang-Baxter equation in promoting the advancement of mathematics. These results have their own characteristics, and together they reflect the important position of Yang-Mills and other theories in the field of mathematics.

With the help of Hitchin's research results, Wu Baozhu confirmed the key theorem of Langlands Program and won the Fields Medal in 2010. This achievement is inseparable from the promotion of Yang-Mills' theory.

The combined research results of Friedan and Donaldson revealed the existence of peculiar differential structures in the four-dimensional space R⁴. At the same time, Yang-Mills theory has unique application value in the field of low-dimensional topology.

The relationships between these tasks are intricate and closely linked. Mathematics and physics are intertwined and closely connected.

In such an interactive relationship, scientific research is like an interconnected network.

Research in physics continues to inspire innovation in the field of mathematics, and achievements in mathematics help further exploration in physics, providing tools and theoretical explanations. For example, Wu Baozhu achieved important breakthroughs by using mathematical results related to physics.

Yang Zhenning’s research goes beyond the formulation and development of theories.

In 1993, he and Deng Yuefan jointly used computers to study a variant of the Hualin problem proposed in Yang Wuzhi's doctoral thesis.

Research has found that within the range of integers not exceeding one billion, any number can be expressed as the sum of no more than 5 pyramid numbers. Moreover, some larger numbers can be represented by no more than 4 pyramid numbers.

This shows that computers have begun to penetrate deeply into the research of basic disciplines.

With the help of modern computing methods, ancient mathematical problems were explored and new discoveries were made, which fully reflects the powerful power of integration between disciplines.

This achievement is expected to inspire many scientists to try new research methods and tools when exploring traditional mathematical problems.

The research results of many scientists such as Chen Ning Yang, on the one hand, demonstrate the profound impact of physics on mathematics, and on the other hand, they also highlight the outstanding leadership role of outstanding scientists in interdisciplinary research.

Can you think of any other researchers who have had such a significant impact at the intersection of different disciplines?