Around 4000 BC, digital inscriptions appeared on pottery in Anbanpo, Xi 'an, China.
From 3000 BC to 65438 BC+0700 BC, mathematical records appeared on Babylonian clay tablets.
In 2700 BC, in the era of the Yellow Emperor in China, it was said that Li Shou did arithmetic and invented Jiazi.
Before 2500 BC, according to "Dead Body" written by Shijiao in China during the Warring States Period, "the ancients (note: the legendary Huangdi or Shi Yao people) were rules, moments, accuracy and ropes, which made the world follow suit", which is equivalent to the existing concept of "round, square, flat and straight".
In 2 100 BC, the vertical and horizontal chart of Hetuluo letters, which symbolizes good luck, appeared in the Xia Dynasty in China, and was called "Jiugongsuan", which was regarded as the oldest discovery of modern combinatorial mathematics.
Mesopotamia had a multiplication table that used hexadecimal arithmetic.
From 1900 BC to 1600 BC, mathematical records appeared in ancient Egyptian papyrus, and a decimal-based notation appeared, which simplified multiplication into fractional calculation of arithmetic and addition. There are methods to measure the area of triangle and circle, the volume of pyramid and frustum.
By BC 1950, Babylonians had already solved binary linear equations and quadratic equations, and they already knew Pythagorean theorem.
In BC 1400, Oracle Bone Inscriptions in China, Oracle Bone Inscriptions and Yin Dynasty had decimal notation, and the most was 30,000.
In BC 1050, during the Western Zhou Dynasty in China, "Nine Numbers" became one of the compulsory courses of "Guo Zi".
In the 6th century BC, Thales of ancient Greece developed elementary geometry and began to prove geometric propositions.
The Pythagorean school of ancient Greece believes that number is the source of all things, and the organization of the universe is a harmonious system of numbers and their relationships. Pythagorean theorem was proved and irrational numbers were discovered, which caused the so-called first mathematical crisis.
Indians look for sqrt (2) =1.4142156.
Around 462 BC, Zhi Nuo and others of Italian Elijah School pointed out various contradictions in movement and change, and put forward Zeno's paradox about time, space and number (parmenides, Zhi Nuo, etc. In ancient Greece).
In the 5th century BC, Hippocrates of Qiu Si, ancient Greece, studied the area of a plane figure surrounded by straight lines and arcs, and pointed out that the area of a similar bow was proportional to the square of its chord. Began to arrange geometric propositions in a scientific way.
In the 4th century BC, eudoxus of ancient Greece extended the proportional theory to incommensurable quantities and discovered the "exhaustive method". Begin to make deductive arrangements according to the axioms in mathematics.
Democritus School in ancient Greece used "atomic method" to calculate area and volume. A line segment, an area or a volume is considered to be composed of many inseparable "atoms". The quadratic curve is put forward and the oldest solution of cubic equation is obtained.
Aristotle in ancient Greece established the Aristotle School and began to make a comprehensive study of mathematics and zoology.
In 400 BC, Mo Jing in China during the Warring States Period recorded some geometric principles.
In 380 BC, Plato School in ancient Greece pointed out the role of mathematics in training thinking and studied the measurement of regular polyhedron and incommensurability.
In 350 BC, Menarque Moss of ancient Greece discovered three kinds of conic curves and used them to solve the cube problem. In ancient Greece, xenophobia began to write the history of geometry. Thelmalidas in ancient Greece created a simple equation of the world.
In 335 BC, Odysseus of ancient Greece began to write the history of mathematics.
In the 3rd century BC, the 13th volume of Euclid's Elements of Ancient Greek Geometry was published, which systematized the discoveries of predecessors and himself, established the logical system of geometry, and became the earliest axiomatic mathematical work in the world.
In the third century BC, Archimedes of ancient Greece studied the area and volume surrounded by curve figures and curves. The paraboloid, hyperboloid and ellipse are studied, the relationship between cylinder, cone and hemisphere is discussed, and the spiral is also studied.
In China during the Warring States Period, calculation became the main calculation method at that time; There are some examples of limit concept, fractional operation, special angle concept and game theory recorded in Zhuangzi and Kao Gong Ji.
In 230 BC, Eratosthenes of ancient Greece put forward the concept of prime number and invented the screening method for finding prime numbers.
From the 3rd century BC to the 2nd century BC, Apolloni in ancient Greece published eight works on conic curves, which were the earliest works on ellipses, parabolas and hyperbolas.
In BC 170, the bamboo slips calculation book "Calculation Book" appeared in Hubei.
In 150 BC, Hippocrates in ancient Greece began to study spherical triangles, which laid the foundation of trigonometry.
Around the first century BC, China's Weekly Parallel Calculations was published. Among them, the theory of "covering the sky", the use of quarter calendar method, fractional algorithm and open method are expounded.
The first year of AD ~ AD 1000.
In 50- 100 A.D., following the revision by Zhang Cang and Geng Shouchang in the Western Han Dynasty, Nine Chapters of Arithmetic was compiled in the Eastern Han Dynasty, which was the earliest mathematical monograph in China and collected the answers to 246 questions.
In 75 AD, Helen of ancient Greece studied the calculation method and expansion method of area and volume, and put forward Helen formula.
About a century ago, Menelao of ancient Greece published The Science of the Ball, which included the geometry of the ball and discussed the spherical triangle.
Hilong in ancient Greece wrote an encyclopedia about geometry, calculation and mechanics. In metrology, the "Shilong formula" of triangle area is calculated in geometric form.
About 100, Nicomark in ancient Greece wrote Introduction to Arithmetic, and since then, arithmetic has become an independent subject.
Around 150, Ptolemy of ancient Greece wrote "Mathematical Compendium", found that pi was 3. 14 166, and put forward the perspective projection method on the sphere and the discussion of latitude and longitude, which is an example of ancient coordinates.
In the third century, all the ancient Greek maps were written into thirteen volumes of algebraic arithmetic, six of which have been preserved to this day, and many definite and indefinite equations have been solved.
From the 3rd century to the 4th century, during the Wei and Jin Dynasties, Zhao Shuang of China listed the proposition ***2 1 about the trilateral relationship of right triangle in Notes on Pythagoras Square.
Liu Hui of China invented secant, and calculated pi as 3.1416. The book island calculation classics discusses the calculation method of island distance and height.
In the 4th century, Pappus's geometric work "Mathematical Integration" came out, which is a manual for the study of ancient Greek mathematics.
In about 463, Zu Chongzhi of China calculated the approximate value of pi to the seventh place after the decimal point, which was more than 1000 years earlier than in the west.
From 466 to 485 AD, Zhang Qiujian wrote it in the Three Kingdoms period of China.
In the 5th century AD, Indian Ayabata wrote a book on mathematics and astronomy, in which he discussed the solution of an indefinite equation, metrology and trigonometry, and made a sine table.
In 550, Zhen Luan of the Southern and Northern Dynasties in China wrote Five Grass Calculations, Five Classics Calculations and Arithmetic Records.
In the 6th century, during the Six Dynasties in China, China's ancestor (Riheng) put forward the law of ancestors: if the cross-sectional areas of two equal heights are equal, the volumes of the two are equal. It was not until17th century that the same law was discovered in the west, which was called cavalieri's principle.
"Interpolation" was used to calculate the correct positions of the sun and the moon in the Huang Ji calendar of the Sui Dynasty (Liu Zhuo, China).
In 620, Wang Xiaotong of the Tang Dynasty in China wrote The Classic of Ancient Calculations, which solved the problem of finding the positive root of cubic equation proposed in large-scale earthwork.
In 628, Brahmagupta of India studied definite equation and indefinite equation, quadrilateral, pi, trapezoid and sequence. The first general solution of the equation ax+by=c(a, b and c are integers) is given.
In 656 AD, China Tang Dynasty and Li Zhuan wrote Notes on Ten Calculations as a textbook for imperial academy Mathematics Museum. Ten Arithmetic Classics refers to Zhou Xun, Nine Chapters Arithmetic, Arithmetic Classics of Island, Arithmetic Classics of Zhang Qiu, Arithmetic of Five Classics, etc.
In 727, during the Kaiyuan period of the Tang Dynasty in China, monks and their party compiled the Dayan Calendar and established the unequal interpolation formula.
In 820, Al-Rashid submodule of Arabia published the Indian counting algorithm, which made Western Europe familiar with the decimal system.
In 850, Mokpiro of India put forward the algorithm of ridge.
In about 920, Al Albatani of Arabia put forward the concepts of tangency and cotangent, and from 0? To 90? In this paper, sine is used to mark sine, and sine theorem is proved.
A.D. 1000 ~ 1700
1000 ~ 10 19 years, Liu Yi of the northern song dynasty in China wrote the theory of the origin of ancient times, and put forward the "pros and cons".
1050, Jia Xian of Song Dynasty in China created "the method of increasing, multiplying and opening any higher power" and listed the binomial theorem coefficient table, which was an early discovery of modern combinatorial mathematics. The so-called "Yang Hui Triangle" refers to this method.
From 1086 to 1093, Shen Kuo of China in Song Dynasty put forward "gap product" and "meeting circle" in Meng Qian's Bi Tan, and began to study high-order arithmetic progression.
1079, Kayam of Arabia completed a book "Algebra", systematically studied cubic equations, and solved cubic equations with conic curves.
1 1 century, Al Karhi of Arabia solved the root of quadratic equation for the first time.
1 1 century, the Egyptian Al Haissam solved the "Haissam" problem, that is, two lines on a circular plane should intersect at a point on the circumference and form an equal angle with the normal of that point.
/kloc-in the 0/2nd century, the Indian Maijialuo wrote the book Risawati, which is an important work in oriental arithmetic and calculation.
1202, Peponacci of Italy published The Book of Calculations, which introduced Indo-Arabic symbols to the West.
1220, Peponacci of Italy published the book Geometry Practice, which introduced many examples that were not found in Arabic materials.
1247, Qin of the Song Dynasty in China wrote * * * 18 "Shu Shu Jiu Zhang", which popularized the multiplication, division and expulsion methods. The solution of the simultaneous congruence formula proposed in the book is more than 570 years earlier than that in the west.
During the period of 1248, China Song Dynasty Li Zhi wrote twelve volumes of "Measuring the Circle Sea Mirror", which was the first work to systematically discuss "Tianshu".
126 1 year, Yang Hui of Song Dynasty in China wrote "Detailed Explanation of Nine Chapters Algorithm", and used "superposition" to find the sum of several kinds of higher-order arithmetic progression.
1274, Yang Hui of the Song Dynasty in China published the book Multiplication, Division and Change, which described the agile method of "nine returns" and introduced various calculation methods of multiplication and division.
1280, the yuan dynasty "calendar" compiled the sun and moon azimuth table (China, Wang Xun, Guo Shoujing, etc. ) By appealing for differences.
/kloc-Before the middle of 0/4th century, China began to use abacus and gradually replaced it.
1303, Siyuan Jade Mirror, written by Zhu Shijie in China in Yuan Dynasty, was three volumes, which promoted Tianyuan Art to Siyuan Art..
1464, J. Miller of Germany systematically summarized trigonometry in On Various Triangles (published in 1533).
In 1489, German Weidemann uses "+"and "-"to indicate symbols.
1494, Pachouri published Arithmetic Integral, which reflected people's understanding of arithmetic, algebra and trigonometry at that time.
15 14 years, Hejk in the Netherlands used "+"and "-"as symbols for addition and subtraction.
1535, Tattaglia of Italy discovered the solution of cubic equation.
1540, Reckord in Britain means equality with "=".
1545, Italians cardano and Fernow published the general algebraic solution formula of cubic equation in Dafa.
From 1550 to 1572, Bombelli published Algebra, which introduced imaginary numbers and completely solved the algebraic problem of cubic equations.
1585, Steven of the Netherlands put forward the concept and symbol of fractional index; This paper systematically introduces the meaning, calculation method and expression method of decimal and decimal.
Around 159 1 year, the Vedas in Germany used letters to represent the general symbols of numerical coefficients for the first time in Wonderful Algebra, which promoted the general discussion of algebraic problems.
1596, Reticus of Germany defined six trigonometric functions from the relationship between the angles of a right triangle.
1596 ~ 16 13 years, Otto and Pittis kus completed the hexadecimal tables of six trigonometric functions at intervals of 10 second.
16 14 years, Naipur, England, formulated logarithms and made the first logarithms table, only making a circular slide rule and a calculation stick.
16 15 years, Kepler, Germany, published "solid geometry of wine barrels", and studied the rotating volume of conical curves.
1635, cavalieri, an Italian, published The Geometry of Essential Continuum, which avoided infinitesimal and expressed the simple form of calculus in the form of no branches.
1637, Descartes published Geometry, put forward analytic geometry, and introduced variables into mathematics, which became a "turning point in mathematics".
1638, Fermat in France began to solve minimax problems by differential method.
Galileo of Italy published "On Mathematical Proof of Two New Sciences", studied the relationship among distance, speed and acceleration, and put forward the concept of infinite set. This book is regarded as an important scientific achievement of Galileo.
1639, De Shag of France published the draft of "Trying to study what happens at the intersection of a cone and a plane", which is an early work of modern projective geometry.
164 1 year, Pascal of France discovered Pascal's theorem about the hexagon inscribed in a cone.
1649, Pascal of France made Pascal calculator, which is the pioneer of modern computer.
1654, Pascal and Fermat in France studied the basis of probability theory.
1655, Varis published arithmetica infinitorum, which extended algebra to analysis for the first time.
In 1657, Huygens of the Netherlands published an early paper on probability theory, on calculus of probability games.
1658, Pascal of France published "General Theory of Cycloids", which made a full study of "Cycloids".
In 1665 ~ 1676, Newton (1665 ~ 1666) lived in Leibniz (1673 ~ 1676) and Leibniz (/).
1669, Newton and Raphson in Britain invented Newton-Raphson method for solving nonlinear equations.
1670, Fermat of France put forward Fermat's last theorem.
1673, Huygens in the Netherlands published an oscillating clock, in which the evolute line and the evolute line of a plane curve were studied.
1684, Leibniz, Germany, published a book about differential method, which is a new method for finding minimax and tangents.
1686, Leibniz, Germany, published a book about integration methods.
169 1 year, Jean Bernoulli of Switzerland published Elementary Differential Calculus, which promoted the application and research of calculus in physics and mechanics.
1696, Robida of France invented the "Robida Rule" for finding the limit of infinitives.
1697, johann bernoulli solved some variational problems and discovered the steepest descent line and geodesic line.
AD 170 1 ~ 1800。
1704, Newton published the counting of cubic curves, and used infinite series and flow number method to find the area and length of curves.
17 1 1 year, Newton published "Analysis of Using Series and Flow Number". .
17 13, Jaya Bernoulli of Switzerland published the first book on probability theory, Guess.
17 15 years, Boo Taylor of Britain published the incremental method, etc.
173 1 year, a Frenchman, Crelo, published The Study of Double Curvature Curves, which was the first attempt to study spatial analytic geometry and differential geometry.
1733, the normal probability curve was discovered by De Le Havel in Britain.
1734, British Becker published "Analytical Scholars" with the subtitle "To Mathematicians who don't believe in God", attacking Newton's flow method, which caused the so-called second mathematical crisis.
1736, Newton published the method of flow number and infinite series.
1736, Euler of Switzerland published the Theory of Mechanics or Analytic Description of Motion, which is the first work to develop Newton's particle dynamics by analytical method.
1742, maclaurin of Britain introduced the power series expansion method of functions.
1744, Euler of Switzerland deduced Euler equation of variational method and found some minimal surfaces.
1747, French D'Alembert and others initiated the theory of partial differential equations from the study of string vibration.
From 65438 to 0748, Euler of Switzerland published the Outline of Infinite Analysis, which is one of Euler's major works.
From 1755 to 1774, Euler of Switzerland published three volumes of differential and integral. This book includes the theory of differential equations and some special functions.
From 1760 to 176 1, Lagrange of France systematically studied the variational method and its application in mechanics.
1767, Lagrange of France discovered the method of separating the real roots of algebraic equations and the method of finding their approximate values.
1770 ~ 177 1 year, Lagrange of France used permutation groups to solve algebraic equations, which was the beginning of group theory.
1772, Lagrange of France gave the initial special solution of three-body.
1788, Lagrange of France published Analytical Mechanics, which applied the newly developed analytical methods to the mechanics of particles and rigid bodies.
1794, Legendre, France published a widely circulated elementary geometry textbook "Geometry Outline".
Gauss of Germany put forward the least square method from the study of measurement error, which was published in 1809.
1797, Lagrange of France published analytic function theory, and established differential calculus without limit concept by algebraic method.
1799, French gaspard monge founded descriptive geometry, which has been widely used in engineering technology.
Gauss of Germany proved a basic theorem of algebra: algebraic equations with real coefficients must have roots.
AD 1800 ~ 1899
180 1 year, Gauss of Germany published Arithmetic Research, which initiated modern number theory.
1809, gaspard monge published the first book of differential geometry, The Application of Analysis in Geometry.
18 12, Laplace of France published the book Analytical Probability Theory, which is a pioneer of modern probability theory.
18 16, Gauss of Germany discovered non-Euclidean geometry, but it was not published.
182 1 year, Cauchy published an Analysis Course, which strictly defined the continuity, derivatives and integrals of functions with limits and studied the convergence of infinite series.
1822, French poinsettia system studied the invariance of geometric figures under projection transformation and established projective geometry.
French Fourier studied heat conduction and invented Fourier series to solve boundary value problems of partial differential equations, which had great influence on theory and application.
1824, Abel of Norway proved that it is impossible to solve the quintic equation with roots.
1826, Abel of Norway discovered that the series sum of continuous functions is not continuous functions.
Russian Lobachevsky and Hungarian Poirot changed the parallel axiom in Euclidean geometry and put forward the theory of non-Euclidean geometry.
From 1827 to 1829, Jacoby of Germany, Abel of Norway and Le Adel of France established the theory of elliptic integral and elliptic function and applied it to physics and mechanics.
1827, Gauss of Germany established the system theory of surfaces in differential geometry.
Mobius of Germany published gravity center calculus and introduced homogeneous coordinates for the first time.
In 1830, Porzano of Czech Republic gave an example of a so-called "ill-conditioned" function, which is continuous and has no derivative.
French Galois established group theory when he studied whether algebraic equations could be solved by roots.
183 1 year, Cauchy of France discovered the convergence theorem of analytic function power series.
Gauss of Germany established the algebra of complex numbers, and used points on the plane to represent complex numbers, which broke the mystery of complex numbers.
1835, Sturm, France, proposed a method to determine the position of real roots of algebraic equations.
In 1836, Cauchy of France proved the existence of solutions of differential equations with analytic coefficients.
Steiner of Switzerland proved that the figure containing the largest area in all closed curves with known perimeters must be a circle.
1837, Dirichlet of Germany gave a convergence theorem of trigonometric series for the first time.
1840, Dirichlet of Germany applied analytic function to number theory and introduced Dirichlet series.
184 1 year, Jacoby of Germany established the system theory of determinant.
1844, grassmann studied multivariable algebraic system and put forward the concept of multidimensional space for the first time.
1846, Jacobian of Germany put forward the Jacobian method of seeking truth from the eigenvalues of symmetric matrices.
1847, Boolean algebra was founded by British Boolean, which has an important application in later computer design.
In 1848, Kumor studied factorization in various number fields and introduced ideal numbers.
Stokes in Britain discovered an important concept of function limit-uniform convergence, but it was not strictly explained.
1850, Riemann of Germany gave the definition of "Riemann integral" and put forward the concept of function integrable.
185 1 year, Riemann of Germany put forward the principle of * * shape mapping, which has been widely used in mechanics and engineering technology, but it has not been proved.
1854, Riemann of Germany established a wider class of non-Euclidean geometry-Riemann geometry, and put forward the concept of multidimensional topological manifold.
Chebyshev of Russia began to establish the theory of function approximation, and used elementary functions to approximate complex functions. Since the 20th century, due to the application of electronic computers, the theory of function approximation has made great progress.
1856, Wilstrass of Germany established the concept of uniform convergence in limit theory.
In 1857, Riemann in Germany discussed Riemann surfaces in detail, and regarded multivalued functions as single-valued functions on Riemann surfaces.
1868, Pluck introduced some new concepts in analytic geometry, and proposed that lines and planes can be used as basic spatial elements.
1870, Lie of Norway discovered Lie groups, and used Lie groups to discuss the quadrature problem of differential equations.
Kronig of Germany gave the axiomatic structure of group theory, which was the starting point of later research on abstract groups.
1872 mathematical analysis "arithmeticization", that is, real numbers are defined by the set of rational numbers (Detkin, Cantor, Wilstras in German).
German Klein published "Herun Root Program", and regarded every geometry as an invariant of a special transformation group.
1873, Hermite of France proved that E is a transcendental number.
1876, Wilstrass of Germany published the analytic function theory and established the complex variable function theory on the basis of power series.
188 1 ~ 1884, Gibbs of the United States formulated vector analysis.
188 1 ~ 1886, poincare, France published the paper "Integral Curve Determined by Differential Equations" continuously, which initiated the qualitative theory of differential equations.
1882, German Lin Deman proved that pi is a transcendental number.
Hevesey of Britain put forward the operational differential product, which is a simple method to solve some differential equations and is often used in engineering.
1883, Cantor established the set theory and developed the theory of out-of-tolerance cardinality.
1884, flaig published The Basis of Number Theory, which is the beginning of the quantifier theory in mathematical logic.
From 1887 to 1896, Dabble published four volumes of Lectures on the General Theory of Surfaces, summarizing the achievements of differential geometry of curves and surfaces in the past century.
1892, Lyapunov of Russia established the theory of motion stability, which is an important aspect of qualitative theory research of differential equations.
From 1892 to 1899, poincare of France founded the theory of automorphism function.
1895, poincare of France put forward the concept of homology and initiated algebraic topology.
1899, German Hilbert's Fundamentals of Geometry was published, which put forward a strict axiomatic system of Euclidean geometry, which had a great influence on the axiomatic trend of mathematics.
Rayleigh and others first put forward the idea of Monte Carlo method, which is a calculation method based on statistical concepts. In the 1920s, Courant (Germany), von Neumann (USA) and others developed this method, which was widely used in computers.
AD 1900 ~ 1960
1900
Hilbert, a German mathematician, put forward 23 unsolved mathematical problems, which attracted the attention of many mathematicians in the 20th century.
190 1 year
Hilbert, a German mathematician, strictly proved Dirichlet's principle and created a direct method of variational method, which has many applications in engineering technology.
German mathematicians Schur and Frobnius first put forward the representation theory of groups. Since then, the representation theory of various groups has been studied extensively.
Italian mathematicians Qi and Wei Qi Tower basically completed tensor analysis, also known as absolute differential calculus. An analytical tool for studying Riemannian geometry and relativity is established.
Lebesgue, a French mathematician, put forward Lebesgue measure and Lebesgue integral, which extended the concepts of length and area integral.
1903
Bert Russell, a British mathematician, discovered the Russell paradox in set theory, which triggered the third mathematical crisis.
Fridholm, a Swedish mathematician, established the basic theory of linear integral equation, which is a mathematical tool to solve mathematical and physical problems, and prepared for the establishment of functional analysis.
1906
Italian mathematician Severi summed up the study of classical algebraic geometry.
French mathematician Fleischer and Hungarian mathematician Reese took the infinite set of functions as the research object, introduced the concept of function space, and began to form Hilbert space. This is the origin of functional analysis.
German mathematician Haarto Gus began to systematically study the theory of complex variable function with multiple independent variables.
Russian mathematician Markov first put forward the mathematical model of "Markov chain".
1907
German mathematician Cobb proved a basic principle of complex variable function theory-Riemann * * * shape mapping theorem.
Brouwer, a Dutch-American mathematician, opposed the use of law of excluded middle in mathematics and put forward intuitive mathematics.
1908
Geoffrey, a German mathematician, established a point set topology.
German mathematician Zemailuo put forward the axiomatic system of set theory.
1909
Hilbert, a German mathematician, solved the famous Willing problem in number theory.
19 10 year
At the end of 19 and the beginning of the 20th century, German mathematician Steinitz summarized the research of various algebraic systems such as groups, algebras and fields, and created modern abstract algebra.
The Dutch-American mathematician Lu Brouwer discovered the fixed point principle, and later discovered the dimension theorem and simplex approximation method, which made algebraic topology a systematic theory.
British mathematicians Bertrand Russell and Karl Schwartz published the Principles of Mathematics in three volumes, trying to generalize mathematics into formal logic, which is the representative work of modern logicism.
19 13 years
Edgardon of France and Weil of Germany completed the finite-dimensional representation theory of semi-simple Lie algebras, which laid the foundation for the representation theory of Lie groups. This has important applications in quantum mechanics and elementary particle theory.
Weil of Germany studied Riemannian surface and put forward the concept of complex manifold.
19 14 years
Hausdorff of Germany put forward the axiomatic system of topological space, which laid the foundation of general topology.
19 15
Swiss-born German-American Einstein and German karl schwarzschild applied Riemann geometry to the general theory of relativity, and solved the spherical symmetry field equation, so that the motion of Mercury's perihelion can be calculated.
19 18
Hatay and Liduwute in Britain applied the method of complex variable function theory to study number theory and establish analytic number theory.
In order to improve the design of automatic telephone exchange, Ireland in Denmark put forward the mathematical theory of queuing theory.
The Formation of Hilbert's Space Theory (Rees, Hungary).
19 19
German Haenszel established P-adic number theory, which is very important in algebraic number theory and algebraic geometry.
1922
Hilbert of Germany put forward the idea that mathematics should be completely formalized, and established a formalism system and proof theory on the basis of mathematics.
1923
The concept of fiber bundle originated from the differential geometry thought of general connection put forward by French E. Gadang, which unified Klein's and Riemann's geometric views.
Adama of France put forward well-posedness of partial differential equations to solve Cauchy problem of second-order hyperbolic equations ().
Barnaha in Poland put forward a broader theory of function space-Barnaha space ().
Nowiener of the United States put forward a measure of infinite dimensional space-Wiener measure, which played a certain role in probability theory and functional analysis.
1925
Haber Bohr of Denmark founded almost periodic function.
Fisher in Britain initiated "experimental design" (a branch of mathematical statistics) with the background of biology and medical experiments, and also established the basic method of statistical inference.
1926
Germany's NATO basically completed the ideal theory that had a great influence on modern algebra.
1927
Bierhoff of the United States established the system theory of dynamic systems, which is an important aspect of qualitative theory of differential equations.
1928
Richard courant, a German-American, proposed a difference method for solving partial differential equations.
Hatle of the United States first put forward the concept of information in communication.
Grosch of Germany, Ahlfors of Finland and Rafrentiev of the Soviet Union put forward the theory of quasi-* * shape mapping, which has certain application in engineering technology.
1930
Bierhoff of the United States established lattice theory, which is an important branch of algebra and has applications in projective geometry, point set theory and functional analysis.
Von Neumann, an American Hungarian, put forward the spectral analysis theory of self-adjoint operator and applied it to quantum mechanics.
193 1 year
Drumm of Switzerland discovered the relationship between differential forms on multidimensional manifolds and cohomology properties of manifolds, which gave topology an analytical tool.
Austria's Godel proved the incompleteness of axiomatic mathematical system.
Andrei Andrey Kolmogorov of the Soviet Union and Ferrer of the United States developed the theory of Markov process.
1932
French Henri Cartan solved many problems.