Which famous people in the world have their birthdays in September 17?

/kloc-people born in September of 0/7:

Riemann

1September, 826 17, Riemann was born in Breselenz village in Hanover, northern Germany, and his father was a villager.

Poor priest. He began to go to school at the age of six, 14 entered the pre-university study, 19 entered Gotting according to his father's wishes.

The University of Michigan studies philosophy and theology in order to follow in his father's footsteps and become a priest in the future.

Because he loved mathematics since he was a child, Riemann listened to some math classes while studying philosophy and theology. Gottingen at that time

University is one of the mathematical centers in the world. Some famous mathematicians such as Gauss, Weber and Steyr all teach in this university.

Riemann was infected by the atmosphere of mathematics teaching and research here and decided to give up theology and specialize in mathematics.

1847, Riemann transferred to Berlin University and became a student of Jacobi, Dirichlet, Steiner and Eisenstein.

1849 student, returned to Golding University to study for a doctorate, and became a student of Gauss in his later years.

L85 1 year, Riemann received a doctorate in mathematics; 1854, he was hired as a part-time lecturer at the University of G? ttingen. 1857

Promoted to associate professor; 1859, Dirichlet was hired as a professor to replace his death.

Due to years of poverty and fatigue, Riemann began to suffer from pleurisy and tuberculosis less than a month after he got married in 1862.

In the next four years, he spent most of his time in Italy for treatment and rehabilitation. 1866 died in Italy on July 20th at the age of 39.

.

Riemann is one of the most original mathematicians in the history of world mathematics. Riemann's works are few, but extremely profound.

Prints are full of creation and imagination of concepts. Riemann made great contributions to many fields of mathematics in his short life.

Basic and creative work has made great achievements for world mathematics.

The founder of complex variable function theory

/kloc-the most unique creation of mathematics in the 0/9th century is the creation of complex variable function theory, which is the answer to complex numbers in the 0/8th century.

The continuation of the study of number theory. Before 1850, Cauchy, jacoby, Gauss, Abel and Wilstrass were all right.

The theory of single-valued analytic functions has been systematically studied, but for multi-valued functions, only Cauchy and Pisser are somewhat isolated.

Conclusion.

185 1 year, under the guidance of Gauss, Riemann completed his doctoral degree entitled "General Theory Basis of Simple Complex Variable Functions".

Paper, and later published four important articles in the journal of mathematics, which made his doctoral thesis progress.

On the one hand, it summarizes the previous research results of single-valued analytic functions and uses new tools to deal with them.

At that time, the theoretical basis of multivalued analytic functions was established, paving the way for the progress in several different directions.

Cauchy and riemann sum Wilstrass are recognized as the main founders of the theory of complex variable functions, and later proved that

In dealing with the theory of complex variable function, Riemann's method is essential, and Cauchy and Riemann's thoughts are integrated, will

Strass's thought can be deduced from Cauchy-Riemann's point of view.

In Riemann's treatment of multivalued functions, the most important thing is that he introduced the concept of "Riemann surface".

Multi-valued functions are geometrically intuitive through Riemannian surfaces, and the multi-valued functions represented on Riemannian surfaces are single-valued. He is in Li.

In this paper, fulcrum, transverse line and connectivity are introduced into Mann surface, and a series of results are obtained by studying the properties of functions.

Riemann processed complex variable function, single-valued function is an example of multi-valued function, he put some known knots of single-valued function.

Extending this theory to multivalued functions, especially his method of classifying functions according to connectivity, greatly promoted the beginning of topology.

Development period. He studied Abel function, Abel integral and the inversion of Abel integral, and obtained the famous Riemann-

Roche's theorem, the first double rational transformation, constitutes the main content of algebraic geometry developed in 19 century.

In order to perfect his doctoral thesis, Riemann finally gives several applications of his function theory in conformal mapping.

1825 extends the conclusion of conformal mapping from plane to plane to arbitrary Riemannian surfaces, and gives it at the end of the paper.

The famous Riemann mapping theorem is given.

The founder of Riemannian geometry

Riemann's most important contribution to mathematics lies in geometry. He initiated the research and processing of high-dimensional abstract geometry.

The methods and means of geometric problems are a profound revolution in the history of geometry. He established a brand-new method named after it.

The geometric system of word naming has great influence on the development of modern geometry and even the branches of mathematics and science.

1854, Riemann gave a speech to all the faculty and staff in order to obtain additional lecturer qualification at the University of G? ttingen.

Two years after his death (1868), the lecture was published under the title "Assumptions as the Basis of Geometry". give a lecture

He investigated all known geometries, including hyperbolic geometry, a newly born non-Euclidean geometry.

In this paper, a new geometric system is proposed, which is called Riemann geometry.

In order to compete for the prize of Paris Academy of Sciences, Riemann wrote an article on heat conduction in 186 1, which

This was later called his "Paris work". In this paper, his article 1854 is treated technically and further elaborated.

Understand its geometric thought. This article was included in his anthology 1876 after his death.

Riemann mainly studies the local properties of geometric space, and he adopts the way of differential geometry, which is also true in Euclid.

In the geometric or non-euclidean geometry of Gauss, Bolyai and Lobachevsky, space is regarded as a whole.

The consideration is the opposite. Riemann got rid of the curves and curves that Gauss and other predecessors limited geometric objects to three-dimensional Euclidean space.

Based on the surface, a more general abstract geometric space is established from the dimension.

Riemann introduced the concepts of manifold and differential manifold, and called dimensional space manifold. Points in a dimensional manifold can

It is represented by a set of specific values with variable parameters, and all these points constitute the manifold itself. This variable

These parameters are called manifold coordinates, and they are differentiable. When the coordinates change continuously, the corresponding points traverse the flow.

Form.

Riemann defined the distance between two points on manifold, the curve on manifold and the curve between them according to the traditional differential geometry.

Angle. Based on these concepts, the geometric properties of dimensional manifolds are studied. On the dimensional manifold, he also defined

It is similar to the curvature that Gauss described when studying general surfaces. He proved that he has dimensions on dimensional manifolds, and so on.

Third, the situation of Euclidean space is consistent with the results obtained by Gauss and others, so Riemannian geometry is traditional.

Generalization of differential geometry.

Riemann developed Gauss's geometric thought that the surface itself is a space, and carried out the connotation of multidimensional manifold.

The study of nature. Riemann's research led to the birth of another non-Euclidean geometry-elliptic geometry.

In Riemann's view, there are three different geometries. The difference between them is that a given point is used to determine a straight line.

Number of parallel lines made. If only one parallel line can be made, it is called Euclidean geometry; If a person

If not, it is elliptic geometry; If there is a set of parallel lines, you get the third geometry, Robacher.

Vfsky geometry. Riemann therefore developed the space theory after Lobachevsky was closed for more than 1000 years.

The discussion of Euclid's parallel axiom has come to an end. He asserted that objective space is a special manifold with foresight.

Existence of manifolds with some properties. These were gradually confirmed by later generations.

Because Riemann considers the geometric space of any dimension, it is more practical for complex target space.

Value. So in high-dimensional geometry, because of the complexity of multivariable differentiation, Riemann took some different hands from his predecessors.

Paragraph makes the expression more concise, and finally leads to the birth of modern geometric tools such as tensor, external differential and connection. [Name] Albert Einstein (Jewish theoretical physicist)

It is the successful application of Riemann geometry as a tool that makes general relativity geometric. Now, Riemannian geometry has become modern.

The necessary mathematical foundation of theoretical physics.

Creative contribution of calculus theory

Riemann not only did pioneering work in geometry and complex variable function, but also perfected it at the beginning of19th century.

The outstanding contribution of calculus theory goes down in history.

From the end of 18 to the beginning of 19 century, mathematics began to care about the concept and proof of calculus, the largest branch of mathematics.

The Ming dynasty was not rigorous. Porzano, Cauchy, Abel, Dirichlet, and then to Wales,

They are all committed to rigorous analysis. Riemann studied mathematics with Dirichlet at the University of Berlin.

Moreover, he has a deep understanding of Cauchy and Abel's work, so he has his own unique views on calculus theory.

1854, Riemann needed to submit an article reflecting his academic level in order to obtain the qualification of a supernumerary lecturer at the University of G? ttingen.

Newspapers. What he handed in was an article about the possibility of expressing functions by trigonometric series. This is an article.

A masterpiece with rich contents and profound thoughts has a far-reaching influence on perfecting analytical theory.

Cauchy once proved that continuous functions must be integrable, and Riemann pointed out that integrable functions are not necessarily continuous. About Lian

About the relationship between continuity and differentiability, Cauchy and almost all mathematicians of his time believed this, and in the late 1950s,

In the middle of the year, many textbooks "prove" that continuous functions are indispensable. Riemann gives a continuous and non-differentiable

The famous counterexample finally explains the relationship between continuity and differentiability.

Riemann established the concept of Riemann integral described in calculus textbooks, and gave the existence of this integral.

Necessary and sufficient conditions.

Riemann studied Fourier series in his own unique way, popularized Dirichlet and ensured the establishment of poirier expansion.

Lai condition, that is, Riemann condition on convergence of trigonometric series, leads to a series of theorems on convergence and integrability of trigonometric series.

Reason. He also proved that the terms of any conditionally convergent series can be rearranged appropriately so that the new series converges to any specified series.

And/or diverge.

Cross-century achievements of analytic number theory

An important development of19th century number theory is the introduction of analytical methods and results initiated by Dirichlet.

Riemann, on the other hand, pioneered the study of number theory with complex analytic functions and achieved cross-century results.

1859, riemann published the paper "the number of prime numbers under a given size". This is an article of less than ten pages.

The content of the paper is extremely profound. He attributed the distribution of prime numbers to the problem of function, which is now called Riemann function.

Count. Riemann proved some important properties of functions, and simply asserted other properties without proof.

More than a hundred years after Riemann's death, many of the best mathematicians in the world tried their best to prove him.

These assertions, and in the process of making these efforts, have created a new and rich new branch of analysis. at present

Except for one of his assertions, the rest were solved as Riemann expected.

That unsolved problem is now called "Riemann conjecture", that is, all zeros in the belt region are at zero.

In this line (the eighth of Hilbert's 23 questions), this problem has not been proved so far. For some people.

In other fields, members of the Bourbaki school have proved the corresponding Riemann conjecture. The solution of many problems in number theory depends on

In the solution of this conjecture. Riemann's work not only helps to analyze the theory of number theory, but also greatly enriches the complex.

The content of variable function theory.

Pioneer of combinatorial topology

Before the publication of Dr. Riemann's paper, combinatorial topology had some scattered results, among which Euler path was the most famous.

Euler theorem of the relationship among vertices, edges and faces of a closed convex polyhedron. Others seem simple and can't be obtained for a long time.

The problems solved, such as the problem of the seven bridges in Konigsberg and the four-color problem, prompted people to pay attention to combinatorial topology (at that time)

Called positional geometry or positional analysis). But the biggest driving force of topology research comes from Riemann's

The work of complex variable function theory.

Riemann emphasized the necessity of research in his doctoral thesis of 185 1 and in the study of Abelian function.

To study functions, some theorems of position analysis are necessary. According to modern topological terminology, Riemann events

In fact, closed surfaces have been classified by genus. It is worth mentioning that in his dissertation, he talked about some functions.

The idea that all people (at a spatial point) form a connected closed area is the earliest functional idea.

Betty, a professor of mathematics at the University of Pisa, once met Riemann in Italy. Riemann was ill at that time, and so was he.

Unable to further develop his ideas, he passed on these methods to Betty. Betty extended the topological classification of Riemannian surfaces to high.

D graphic connectivity, and made outstanding contributions in other fields of topology. Riemann is a well-deserved combination promotion.

The pioneer of robots.

Open Source Contribution of Algebraic Geometry

/kloc-In the second half of the 9th century, people studied the double rational transformation created by Abel integral and Abel function in Riemannian.

This method has aroused great interest. At that time, they called the study of algebraic invariants and birational transformations algebraic geometry.

In the paper of 1857, Riemann thinks that all equations (or surfaces) that can be transformed into each other belong to one class.

They have the same genus. Riemann calls the number of constants "quasi-modules", and the constants are not under the double rational transformation.

Variable. The concept of "quasi-module" is a special case of "parametric module", and the research on the structure of parametric module is the hottest in modern times.

One of the fields of doors.

Clebsch, a famous algebraic geometer, later came to the University of G? ttingen as a professor of mathematics, and he became more familiar with it.

Riemann's work, and give new development to Riemann's work. Although Riemann died young, it is universally acknowledged that research

The first big step of curve birational transformation is caused by Riemann's work.

Rich achievements in mathematical physics, differential equations and other fields.

Riemann not only made epoch-making contributions to pure mathematics, but also paid great attention to physics, mathematics and the physical world.

He wrote some papers on heat, light, magnetism, gas theory, fluid mechanics and acoustics. he

He was the first person to deal with shock waves mathematically. He tried to unify gravity and light and study the mathematics of human ears.

Structure. He studied ordinary differential equations and partial differential equations abstracted from physical problems and achieved a series of fruitful results.

Result.

In 1857, Riemann wrote the paper "Supplement to the Function Theory Represented by Gaussian Series".

One was unpublished and later collected in his complete works. He studied hypergeometric differential equations and discussion bands.

Order linear differential equations with algebraic coefficients. This is an important document about the singularity theory of differential equations.

/kloc-In the second half of the 9th century, many mathematicians spent a lot of energy on Riemannian problems, but they all failed until 1905.

Hilbert and Kellogg gave a complete solution for the first time with the help of the integral equation theory developed at that time.

Riemann has also made great achievements in the study of automorphic functions in the theory of ordinary differential equations, in his 1858 ~ 1859.

In the lectures on hypergeometric series and the posthumous work on minimal regular surfaces published in 1867, he established the second study.

Automorphic function theory introduced by order linear differential equation is now commonly known as Riemann-Schwartz theorem.

In the theory and application of partial differential equations, Riemann creatively put forward solutions in the papers from 1858 to 1859.

The new method of initial value problem of wave equation simplifies the difficulty of many physical problems. He also popularized Green's theorem; correct

Dirichlet's principle on the existence of solutions of differential equations has done outstanding work, ...

Lectures on partial differential equations used by Riemann in physics were later published by Weber as Differential Equations in Mathematical Physics.

Edited and published, this is a historical masterpiece.

However, Riemann's creative work was not unanimously recognized by the mathematics community at that time, on the one hand, because of his thoughts.

It was too deep for people at that time to understand. Without the concept of free motion, Riemannian space with very large curvature will be difficult to connect.

By, until the emergence of general relativity to quell the blame; On the other hand, some of his work is not rigorous enough, such as

When demonstrating Riemann mapping theorem and Riemann-Roche theorem, Dirichlet principle was abused, which once caused many problems.

Controversy.

Riemann's work directly influenced the development of mathematics in the second half of the19th century, and many outstanding mathematicians re-demonstrated Li.

Under the influence of Riemann's thought, many branches of mathematics have made brilliant achievements.

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World Cup players

Ali Akbar Akbar Sadri was born in 1965.

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