Alberta, I will give a general echelon ranking according to my personal understanding of the history of mathematics, for reference only:
The first echelon [refers to veteran leaders]
Euler, Gauss, Newton, Riemann
These four mathematicians are all the echelon of God, and the contribution of any one is extremely important, and their contribution is not only in the field of mathematics, but also in the field of physics.
For example, Leibniz and Newton invented calculus at the same time, but Leibniz was not as famous as Newton. Although the calculus invented by Leibniz is more practical than Newton, its influence is not as good as Newton's.
However, Euler and Gauss have made unparalleled contributions in the field of basic mathematics, and they are almost equal. Nowadays, the contributions of Euler and Gaussian can be seen everywhere in the scientific field, such as Euler equation, Euler constant, Gaussian distribution, Gaussian law and so on.
Riemann's contribution in the field of advanced mathematics paved the way for many disciplines, such as Riemann geometry, which provided a mathematical basis for the theory of relativity. Concepts such as Riemannian integral, Riemannian manifold and Riemannian condition can be seen everywhere in the field of higher mathematics.
second echelon
Euclid, Archimedes, Poincare, Hilbert, Leibniz, Chen Shengshen, Cantor, Galois, Cauchy, Descartes, von Neumann, Lagrange and so on.
There are many mathematicians who can rank in the second echelon, among whom some have made pioneering contributions to basic mathematics, such as Euclid and Archimedes; Others have made extremely important contributions in their respective fields, such as Chen Shengshen, the father of differential geometry, and Galois, the pioneer of group theory; There are also many versatile figures, such as Poincare, von Neumann, Hilbert and Leibniz.
Mathematicians of the second echelon have made pioneering contributions in at least a certain field of mathematics, and it is difficult to select six of them for ranking. However, mathematicians with extremely important contributions like Euclid and Hilbert still sit firmly in the top ten.
In addition, there are some mathematicians who have made outstanding contributions to a certain point in mathematics and are also very famous, such as:
(1) andrew wiles, the prover of Fermat's last theorem;
(2) emmy noether, the greatest female mathematician, is known as "the mother of modern mathematics";
(3) Turing, the father of artificial intelligence, made great contributions to computers.
(4) Godel, whose achievements in modern logic are extraordinary, is an immortal milestone in mathematics;
..... and so on.
The answer to this question is not unique. What is a great mathematician? In my opinion, great mathematicians should have the following characteristics: first, make great contributions to the development of mathematics; Second, they should lead a group of mathematical talents; Third, solve the key problems in this field; Fourth, establish branches of disciplines.
The following is my ranking of the top ten mathematicians in human history according to the above criteria:
10th place: Hilbert (1862—1943)
German mathematician David Hilbert. He put forward 23 mathematical problems that mathematicians should try their best to solve in the new century, which is considered as the peak in the field of mathematics in the 20 th century. The research on these problems has effectively promoted the development of mathematics. Hilbert was one of the figures who had a profound influence on mathematics in the 20th century.
Hilbert trained a group of outstanding mathematicians and made great contributions to the development of modern mathematics. The main research contents include: invariant theory, algebraic number field theory, geometric basis, integral equation and so on. In these fields of mathematics, Hilbert has made great or pioneering contributions.
Ninth place: Cantor (1845—19 18).
German mathematician Georg Cantor. His contributions to mathematics are set theory and super-finite number theory, and he is one of the most outstanding contributions in the field of mathematics from the end of 19 to the beginning of the 20th century. Cantor's revolution in the infinite field of mathematics was almost completed by himself.
Eighth place: Galois (18 1 1 year-1832)
French mathematician Evariste Galois is the founder of group theory, a branch of modern algebra. When he used group theory to solve algebraic equations, he summed up the theory of groups and fields, which was called Galois Group and Theory.
Galois used the method of group theory to discuss the solvability of equations. The whole method is called Galois Theory, which is one of the basic pillars of contemporary algebra and number theory. He systematically explained why there is no formula solution for the equation with more than five degrees, but there is a formula solution for the equation with less than four degrees. Galois made extraordinary contributions.
Seventh place: Descartes (1596—1650)
Rene descartes, a French mathematician, philosopher and physicist, has made great contributions to the development of modern mathematics and is called the father of analytic geometry. But Descartes' greatest contribution is in philosophy. He is one of the founders of modern European philosophy and is known as the "father of modern philosophy".
Descartes' most important contribution to mathematics was the creation of analytic geometry, which laid the foundation for the creation of calculus. Analytic geometry is still one of the important mathematical methods. The establishment of analytic geometry is an epoch-making turning point in the history of mathematics, and the plane rectangular coordinate system is also established.
Sixth place: Riemann (1826—1866)
German mathematician and physicist Bernhard Riemann made great contributions to mathematical analysis and differential geometry, initiated Riemannian geometry, and paved the way for the development of general relativity. In addition, Riemann also made great contributions to partial differential equations and their applications in physics.
Riemann's contribution influenced the development of mathematics in the second half of19th century, and many outstanding mathematicians made many brilliant achievements in the branch of mathematics under the influence of Riemann's thought. His works are few but profound. Riemann function, Riemann integral and Riemann lemma are all named after him.
Fifth place: poincare (1854—19 12)
Henri Poincare, a French mathematician, is recognized as the leading mathematician in the last quarter of19th century and the beginning of 20th century, and also the last all-rounder in the field of mathematics and application. Poincare's outstanding contribution to mathematics has a far-reaching impact on mathematics in the twentieth century and today.
Poincare has made very important contributions in the fields of number theory, algebra, geometry, topology, etc. The most important work is in function theory. He founded the theory of automorphism function, and introduced fuchs group and Klein group to construct the basic domain. He constructed an automorphic function with series and found its practicability.
Fourth place: Newton (1643—1727)
British physicist isaac newton is called an encyclopedic "all-rounder". Newton's contribution to mechanics will not be detailed, mainly in mathematics. Newton's main contributions in the field of mathematics are calculus, generalized binomial theorem, Newton's identity and Newton's method.
The appearance of calculus led to the birth of the branch of mathematical analysis, and further developed into differential geometry, differential equations, variational methods and so on, which also promoted the development of theoretical physics. Calculus is Newton's most outstanding mathematical achievement, and he has made great contributions to analytic geometry and comprehensive geometry.
Third place: Gauss (1777—1855)
German mathematician Johann Carl Friedrich Gauss is one of the founders of modern mathematics. He is considered as one of the most important mathematicians in the world and is called "the prince of mathematics". More than 100 mathematical achievements named after his name "Gauss" are second to none among mathematicians in history.
Gauss has made outstanding contributions in the fields of number theory, algebra, statistics, analysis and differential geometry. He discovered the prime number distribution theorem and the least square method, and obtained the Gaussian bell curve. Gauss summed up the application of complex numbers and derived the concept of triangle congruence theorem. He is also one of the founders of differential geometry.
Second place: Euler (1707—1783)
Swiss mathematician leonhard euler is called "a versatile mathematician". Euler was one of the most outstanding mathematicians in18th century. He not only made contributions in the field of mathematics, but also pushed mathematics into the field of physics. Euler wrote too many classic mathematical works and formula theorems.
Euler is the founder of analytic number theory. He put forward Euler's identity, established the connection between number theory and analysis, and made it possible to study number theory with calculus. He has made outstanding contributions in the fields of number theory, algebra, infinite series, function concept, elementary function, differential equation, geometry and so on.
First place: Archimedes (287 BC-265438 BC+02 BC)
Archimedes, an ancient Greek mathematician, has many other titles and is called "encyclopedic scientist". He, Gauss and Newton are called the three greatest mathematicians in the world. Archimedes made brilliant achievements in mathematics, especially in geometry.
Archimedes' mathematical thought contains calculus, and his theory is very close to modern calculus, including the advanced study of infinity in mathematics, and foresees the birth of calculus. Archimedes' work in geometry enabled Leibniz and Newton to develop perfect calculus.
Note: Leibniz's achievements are the same as Newton's (in the field of mathematics), mainly calculus, which is not listed separately. In addition, Euclid and Archimedes are both leading figures and are no longer listed separately.
This ranking is rarely recognized by the world, and everyone's status as a master of mathematics is different. I think we can arrange it like this.
1. Riemann
Riemann died at the age of 39. He made great contributions to reanalysis and Riemann geometry. Riemann conjecture and Riemann geometry in complex analysis have great influence on physics.
2. Gaussian
The terminator of classical number theory proves the law of quadratic reciprocity in many ways. He is also the pioneer of complex numbers and the master of differential geometry, and the name of Gauss theorem goes down in history.
3. Euler
The great mathematicians in the transitional period from classical mathematics to modern mathematics have obtained many correct mathematical results through some seemingly incorrect mathematical methods, and studied the relationship between prime numbers and integers.
4. Poincare
Pioneer of topology and qualitative theory of differential equations. Also contributed to the theory of relativity.
5. Newton
The inventor of calculus, the founder of Newton's mechanical system, has a master position in mathematics.
6. Archimedes
As a representative figure in the era of classical mathematics and physics, the lever principle is used to calculate the volume of a ball.
7. Qiu Chengtong
The combination of differential geometry and differential equations has made great contributions to the proof of positive energy conjecture of general relativity.
8. Chen Shengshen
Global master of differential geometry, inventor of Chen Ban.
9.lies
Prove Mundell conjecture.
10. andrew wiles
Prove Fermat's last guess.
The ocean of mathematicians is like a bright pearl in the night sky, illuminating the road of human progress. They are the darling of God, the magic of the creator, the symbol of genius and the ladder of human progress.
There are countless great mathematicians who can call with open hands. Moreover, it is really difficult to distinguish the inheritance, continuity, iteration and gradualism of mathematics. Therefore, the following is a brief list of some recognized mathematics masters, in no particular order, for reference only.
1, Hilbert
Hilbert, a famous German mathematician. 1900, at the second international congress of mathematicians held in Paris, he put forward 23 mathematical problems that mathematicians should strive to solve in the new century, which was considered as the commanding heights of mathematics in the 20th century. The study of these problems promoted the development of mathematics in the 20th century and had a far-reaching impact.
The school of mathematics led by Hilbert is a banner. He is called the "uncrowned king" of mathematics and a genius among geniuses.
2. Singing poets and leading singers
German mathematician and founder of set theory. My father is a Danish businessman of Jewish descent, and my mother comes from an artistic family.
Set theory initiated by Cantor is an important revolution in the history of mathematics, which has brought mathematics into a new era.
3. Galois
Galois is a French mathematician, a branch of modern mathematics and the founder of group theory. The problem of solving algebraic equations by roots is completely solved by group theory, and a set of theories about groups and fields is developed from this.
Galois was a genius, but his talent died young. Maybe he is jealous of his talent, and his life is bumpy and regrettable.
4. Riemann
German mathematician and physicist made great contributions to mathematical analysis and differential geometry, some of which paved the way for the theory of relativity.
Riemannian function, Riemannian integral, Riemannian conjecture, Riemannian manifold, Riemannian geometry, etc. It shows that he can come and go freely in mathematics.
5. Euler
Swiss mathematician,/kloc-one of the most outstanding mathematicians in the 8th century. He is the most prolific mathematician in the history of mathematics, and most of his works have become classic works of mathematics.
Euler can be seen everywhere in mathematics, and Euler formula and Euler constant are all familiar smells.
6. poincare
French mathematician, celestial mechanic and philosopher of science, whose research fields involve number theory, algebra, geometry, topology, celestial mechanics, mathematical physics, theory of multiple complex variables, etc.
Poincare is recognized as the leading mathematician in the last quarter of19th century and the beginning of 20th century, and he is the last person who has a comprehensive understanding of mathematics and its application.
7.gaussian
German mathematician, physicist and astronomer, one of the founders of modern mathematics, is considered as one of the most important mathematicians in the history of mathematics.
Gauss, everyone is not too strange. His name is very famous in middle school. He has the title of "prince of mathematics", and is called the three greatest mathematicians in the world together with Archimedes and Newton.
8. Newton
British mathematician, physicist, jazz, president of the Royal Society, all-rounder in all disciplines.
Mr Newton is well known to the general public, especially the story about Apple, which is almost a household name. Unfortunately, his physical fame is far greater than his mathematical fame.
9. Archimedes
The God of Mathematics, together with Euclid and apollonius, is called the three great masters of ancient Greece, and together with Newton, Gauss and Euler, he is called the four great mathematicians in the world.
Archimedes principle, archimedean spiral, Archimedes triangle, etc. They are all well-known in middle school, and there are crown stories that have been passed down to this day.
10, Cauchy, Turing, Descartes, Euclid, Leibniz, Kolmo Gorov, Von Neumann, Godel ...
This sequence can be extended all the time for reference only. For an in-depth understanding of mathematicians, you can refer to relevant documents and materials, and I won't repeat them here.
Above.
First, Riemann.
Second, Gauss.
Third, poincare.
Fourth, Newton.
Fifth, Hilbert.
Sixth, Euler.
Seventh, Andre Andrey Kolmogorov.
Eighth, Descartes.
Ninth, Euclid.
Tenth, Leibniz.
There are many great mathematicians in human history, far more than ten. I also reject this ranking. After all, it is difficult to convince the public no matter how low the ranking is. Mathematics is not the achievement of one person, but the creation of the broad masses of the people. There are many outstanding mathematicians in every branch of mathematics.
Mathematics is like a towering tree. If it is great, it must be the greatest founder and important promoter in all fields. Then let's take a look at the great mathematicians in human history. These people are remembered by history. Of course, it does not rule out that there are some unknown great contributors who have not left a word or even a name in history.
In fact, it is difficult for many mathematicians to distinguish who is more important than who. According to their achievements in mathematics, they can be roughly divided into the following three echelons. People in the first echelon will definitely make it into the top ten. There are many mathematicians in the second echelon and more mathematicians in the third echelon. The following rankings are more focused on the achievements in the field of pure mathematics for reference only.
The first echelon [refers to veteran leaders]
Archimedes, Newton, Gauss, Euler, Riemann, Euclid, Descartes, Leibniz, Lagrange, Galois, Poincare, Hilbert, Cantor. ...
second echelon
Godel, Alvarez, Napier, jacobin Bernoulli, Fourier, Cauchy, Boolean, Gloria, Leberg, China, Mandelbrot, Liu Hui, johann bernoulli, Laplace, Poncelet, Hamilton, Tao Zhexuan, Nott, Abel, Bayes, Weisstras, etc.
the third echelon
Pythagoras, Jia Xian, Zu Chongzhi, Diophantine, Fibonacci, Veda, Fermat, Pascal, Thales, Goldbach, daniel bernoulli, Poisson, Dirichlet, Augustus de Morgan, Sylvester, Stokes, Hermite, Jordan, Lee, Minkowski, Hardy, Weil, joseph liouville, Qiu Chengtong, wiles and so on.
Up to now, among the top ten greatest mathematicians, I think different people may have different answers, but a few people will rank in the top ten anyway, such as Newton, Euler and Gauss. ..........................................................................................................................
1, isaac newton
In my mind, I put Newton in the first place because he founded calculus. Although calculus was founded by Newton and Leibniz, Newton's notes were earlier than Leibniz's, and calculus promoted the society unprecedentedly.
Newton's achievements in mathematics: he discovered binomial theorem and founded calculus. In addition, Newton also made outstanding contributions to analytic geometry and comprehensive geometry.
Newton is more famous in physics than in mathematics.
Newton's achievements in physics: gravity; Newton's three laws of motion and his achievements in optics found that white light is composed of different colors of light; A prototype of reflecting telescope was made. Put forward the "particle theory" of light.
2. Gaussian
Gauss is known as the "prince of mathematics". The most popular story is that when he was 10, Gauss worked out the algebraic problems of all integer sums from 1 to 100 with very simple methods and very fast speed. Gauss's achievements in mathematics cover all fields of pure mathematics and applied mathematics, and he has made pioneering contributions in algebra, number theory, non-Euclidean geometry, differential geometry and complex variable functions. He also applied mathematics to the study of astronomy, geodesy and magnetism, and he also invented the "least square principle".
The most famous Gaussian distribution is Gaussian distribution, also called normal distribution. Gaussian distribution is the most important distribution in the field of mathematics, and its formula is
3. Archimedes
Archimedes was an ancient Greek mathematician, philosopher, mechanic and astronomer, and was called "the father of mechanics".
Archimedes' most famous achievement is Archimedes' law of buoyancy. In addition, his achievements in mathematics are countless, leaving more than 10 mathematical manuscripts. Archimedes' main achievement is in geometry. He created formulas for finding the far area, surface area and volume of a sphere by "approximation method", and he also found the value of π between 3. 14 168 by secant method. And studied the nature of the spiral, which was called "archimedean spiral" by later generations.
4. Euler
Euler is a Swiss mathematician and a student of Bernoulli, a great mathematician. Euler is the most prolific and outstanding mathematician in the history of science. He wrote 886 books and 886 papers in his life. Euler's writing is easy to understand, and his books such as Introduction to Differential Analysis, Differential Method and Integral Method are all examples of textbooks. He also wrote textbooks for primary and secondary schools in many languages.
Euler's contribution to mathematics is various, and his name can be seen in almost every field. In geometry, there are: Euler line, euler theorem, Euler transformation formula; Algebra and analysis include: Euler solution, Euler function, Euler equation, Euler constant, Euler equation, Euler formula, etc.
In addition, Euler also founded analytical mechanics, rigid body mechanics and other mechanical disciplines, which deepened the design and calculation theory of telescopes and microscopes.
Other mathematicians
Newton, Gauss, Archimedes and Euler are the greatest mathematicians in my mind, and they are in the first echelon of all mathematicians. In addition, my idea of 5- 10 includes Leibniz, Riemann, Euclid, Cauchy, Fermat and Hilbert.
Sometimes it is difficult for us to rank their achievements. As far as mathematics is concerned, some mathematicians have made outstanding achievements in a certain field of mathematics. For a huge mathematics discipline, we can't be familiar with every field, so we don't know much about the contribution of mathematicians in this field, and the ranking is inevitably biased.
Besides the mathematicians mentioned above, there are many great mathematicians we are familiar with, such as Pythagoras, Bernoulli, Lagrange, Laplace, Cantor and Poincare. .......
1. Archimedes (287 BC-265438 BC +02):
Ancient Greek mathematician and mechanic. Firstly, the sphere area, sphere volume, parabola and ellipse area are calculated by "approximation method". This laid the foundation for the emergence of calculus later. Recently, it is found from his manuscript that Archimedes' methodology is "very close to modern calculus" and there is a profound study of infinity in mathematics.
Newton (1643- 1727):
No one denies that Newton was a great mathematician. He is one of the inventors of calculus.
Leibniz (1646- 17 16):
One of the inventors of calculus, we are all following his calculus symbols today. Leibniz was also one of the inventors of binary system. It is said that his inspiration for inventing binary came from China Fuxi Eight Diagrams. Moreover, it is said that he once suggested through missionaries that Emperor Kangxi of the Qing Dynasty in China set up an academy of sciences in Beijing.
4. Euler (1707- 1783):
The most prolific mathematician in history. Formulas, theorems and important constants named after Europe can often be seen in various fields of mathematics. He has strong anti-interference ability, is absorbed in his work, is never disturbed by noise and murmur, and is as cool as a cucumber. I think this more or less provides a reference for contemporary mathematicians who have to be confined to all kinds of secular things. Moreover, it is said that he has a noble style and is willing to support the younger generation.
5. Fourier transform (1768- 1830):
Fourier transform has become one of the most important mathematical tools in engineering, mathematics and other fields. Unfortunately, undergraduate mathematics education in China University seems to despise Fourier transform. Generally speaking, college mathematics graduates don't seem to really understand and use Fourier transform (although they do know its definition and some properties). Therefore, it seems that Fourier transform should be specially offered in the undergraduate education stage of college mathematics.
6. Gauss (1777— 1855):
A mathematical genius with a wide range of research fields. The discovery of the intrinsic property of Gaussian curvature alone is enough to influence people's understanding of surfaces, not to mention the proof of the basic theorem of algebra.
Abel (1802- 1829):
One of the most legendary gifted mathematicians in history proved the insolubility of quintic equation for the first time and made important contributions to elliptic functions. Hermite said that Abel's follow-up work "will keep mathematicians busy for 500 years".
8. Galois (1811-1832):
Another talented mathematician, the founder of group theory, I think this reason is very good.
9. Riemann (1826- 1866):
Riemann has not published many papers. But a number theory paper puts forward one of the most important conjectures in mathematics: Riemann hypothesis. A speech gave birth to Riemannian geometry.
10. Hilbert (1862-1943): His 23 questions were the focus of mathematicians' work in the 20th century. In mathematical work, the Hilbert space proposed by him alone provides a "living" place for countless mathematical work.
Let's just say that if we really rank mathematicians, Chen Jingrun can rank around 10,000. There are so many mathematicians that ordinary people can't even reach the foot of the mountain all their lives.
Great physicists must be great mathematicians, so the greatest mathematicians need to be selected from the greatest physicists. If I had to choose, it would be Maxwell.