This poem was written by Yang Zhenning to Chen Shengshen in 1975.
First, the full text of poetry
Zan Chen Shi Ji
Is it seamless, and it is cleverly spliced.
One integrated mass, vast and wonderful.
Nature loves geometry and the four forces of fiber energy.
Millennium worries, Ogilvy & Mather, Li Chenjia.
Second, interpret poetry and the stories behind it.
The "eternal worry" comes from Du Fu's poem "Write through the ages and know the gains and losses", while "Europe" celebrates Mr. Chen's historical position, catching up with the four previous geometricians, Euclid, Gauss, Riemann and Gadang. This also gives us a reference. I want to talk about Mr. Chen's contribution and their historical position along this line.
"Ou" means Euclid. Now we usually talk about Euclid, and we are all talking about his mathematical work "Elements of Geometry". In fact, Euclid's original text is called "The Original", which is the original text, including the whole mathematics at that time. Coincidentally, in the 20th century, two great mathematicians in China, Mr. Wang and Mr. Hua, made great contributions to geometry and number theory respectively.
Between "Ou" and "Gao", there is actually a man named Descartes. His introduction of coordinates to study geometry is also a revolutionary progress. "High" is Gaussian. In fact, when he was the director of the Observatory at the age of 50, he made geometry while doing geodesy. He extended Euclid's theorem of sum of interior angles of planar triangles to triangles on surfaces (non-planar). Later, Bonnet extended this formula to the case that polygons and edges can be arbitrary curves. Now, this extension is called Gauss-Bonne theorem.
If Gauss-Bonet theorem is further extended after Gauss, it will talk about Riemann, who is a great number theorist. His Riemann conjecture is the first difficult problem in the current Millennium, and he is also a great function theorist. He introduced the concept of high-dimensional Riemannian space and defined the generalization of high-dimensional Gaussian curvature, which we can now call Riemannian curvature. Riemann's motivation comes from the theory of complex variable function and electromagnetism.
Riemann put forward the concept of high-dimensional space, so the development of high-dimensional Riemann geometry needs to describe the objects in high-dimensional space strictly, which is what we now call manifold. Herman was the first person to define it strictly. Wei Yi. He wrote a book called "The Concept of Riemannian Surfaces", which is to apply Riemannian local ideas to Riemannian surfaces and turn them into a whole, which is equivalent to turning local surfaces into closed surfaces.
Teacher Chen once wrote a well-known report called From Triangle to Manifold, which divided geometry into several eras. One is called "primitive man", which means Euclidean geometry; Later Descartes came, with algebraic tools and tools that can be called "dressing people"; Later, the geometry on manifold appeared, and it became a "modern man". Then in the 20th century, with the concept of manifold, it is natural to ask, how to be a modern person, that is, how to develop the geometry on manifold?
The representative here is Eli? Katan, that is, "Jia of Ou". Jia Dang's main contributions are many, one of which is to extend the theory of local calculus to manifolds, which is called external differential. After finishing his postdoctoral studies in Germany, Mr. Chen chose to go to Paris to be a postdoctoral fellow with Jia, and stayed in Paris for a year, studying Jia's articles hard and getting the essence.
With the development of mathematics, the key to the next step is to extend the most important Gauss-Bonnet in two-dimensional geometry to high dimensions. One of them will encounter a problem, which is to extend the concept of Gaussian curvature to higher dimensions, and then try to prove the desired equation.
The first batch of successes were Allen Dolford and André Weil. André Weil is the founder of bourbaki and one of the greatest mathematicians in the 20th century. Allen Dolford is his colleague. In a sense, their research can be said to have completed the promotion of Gauss-Bonet theorem to a higher dimension, but it is not satisfactory, and it can be said that "we know why, but we don't know why".
Later, in the process of continuing to promote this work, teacher Chen defined the demonstration class Chen Shengshen? Class. This Chen? According to Mr. Chen himself, this is the reason why he suddenly thought of going to the library on a weekend. This may be the master's modest words, but what about Chen Shengshen? The influence of class is obvious to all.
Except Chen? Another influential and pioneering work of Mr. Chen is to define Chen Shengshen. Chen Shengshen-Simmons has a far-reaching influence on the physical level and algebraic geometry level.
In the last sentence, "Ou Gaoli Chen Jia", Yang Zhenning ranks Chen Shengshen with Euclid, Gauss and riemann sum in the history of mathematics, calling him the fifth person in the history of mathematics. This is not well received.
Introduction to Chen Shengshen:
Chen Shengshen (19 1 1 year1October 28th -20041February 3rd), born in Jiaxing, Zhejiang Province, is one of the greatest geometricians in the 20th century, and is known as ". Former first academician of Academia Sinica, American National Academy of Sciences, founding academician of Third World Academy of Sciences, foreign academician of Royal Society, foreign academician of Italian National Academy of Sciences, foreign academician of French Academy of Sciences and the first batch of foreign academicians of China Academy of Sciences.
Chen Shengshen gave the intrinsic proof of the high-dimensional Gauss-Bonne formula, which is usually called Gauss-Bonne-Chen formula. His "Chen Shengshen Class" has become a classic. He developed the theory of fiber bundle, which influenced all fields of mathematics.
He established the theory of value distribution on high-dimensional complex manifolds, including Bot-Chen theorem which influenced algebraic number theory. He laid the foundation of generalized integral geometry and obtained the basic kinematics formula. Chen's characteristic class and Chen's differential formula introduced by him have penetrated into other fields besides mathematics and become important tools of theoretical physics.