◇ Before 600 BC ◇ According to "Dead Bodies" written by 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 imitate", which was equivalent to "round, square, flat and flat" before 2500 BC. About 2 100 BC, Mesopotamia had a multiplication table, in which hexadecimal algorithm was used. Around 2000 BC, there were arithmetic and fractional calculation methods based on decimal notation in ancient Egypt, which simplified multiplication into addition. There are methods to measure the area of triangle and circle, the volume of pyramid and frustum. China Yin Ruins Oracle Oracle Bone Inscriptions recorded decimal notation, the largest number is 30,000. Around BC 1950, Babylonians had been able to solve binary linear equations and quadratic equations, and they already knew Pythagorean theorem. ◇ 600 BC-1 year◇ 6th century BC, elementary geometry developed (Thales, ancient Greece). Around the 6th century BC, the Pythagorean school in ancient Greece believed that numbers were the source of all things, and the organization of the universe was 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. In the 6th century BC, Indians discovered that √ 2 =1.4142156. Around 462 BC, the 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, the area of a plane figure surrounded by a straight line and an arc was studied, and it was pointed out that the area of a similar bow was proportional to the square of its chord (Hippocrates, ancient Greece). In the 4th century BC, the theory of proportionality was extended to incommensurable quantities, and the "exhaustive method" (ancient Greece, eudoxus) was discovered. In the 4th century BC, democritus School in ancient Greece used the "atomic method" to calculate the area and volume. A line segment, an area or a volume is considered to be composed of many inseparable "atoms". In the 4th century BC, the Aristotelian School was founded, which made a comprehensive study of mathematics and zoology (ancient Greece, Aristotle, etc. ) At the end of 4th century BC, the conic curve was put forward, and the solution of the oldest cubic equation was obtained (Minekmo, ancient Greece). In the third century BC, 13 volume of Geometry was published, which systematized the previous and own discoveries and became the masterpiece of ancient Greek mathematics (Euclid, ancient Greece). In the third century BC, the area and volume surrounded by curves and surfaces were studied. Parabolic, hyperboloid and ellipse are studied. The relationship between cylinder and conical hemisphere is discussed. Spiral (ancient Greece, Archimedes) has also been studied. In the 3rd century BC, calculation was the main calculation method in China at that time. From the 3rd century BC to the 2nd century BC, eight books on conic curves were published, which were the earliest works on ellipses, parabolas and hyperbolas (Apollonius, ancient Greece). 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. In 1 century BC, Dai Li recorded an auspicious vertical and horizontal map of Hutuluo in ancient China, which was called "Jiugongsuan" and was regarded as the oldest discovery of modern combinatorial mathematics. ◇1-400◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇9671 About a century ago, he published The Science of the Ball, including the geometry of the ball, in which the spherical triangle was discussed (Menelao in ancient Greece). A century or so, he wrote an encyclopedia about geometry, calculation and mechanics. In metrology, the "seamount formula" of triangle area is calculated in geometric form (seamount in ancient Greece). About 100, Nicomark in ancient Greece wrote Introduction to Arithmetic, and since then, arithmetic has become an independent subject. 150 or so, and π = 3. 14 166. The perspective projection method and the latitude and longitude on the sphere are discussed. This is an example of ancient coordinates (Ptolemy, ancient Greece). In the third century, he wrote thirteen volumes of algebraic arithmetic, six of which have been preserved so far, and solved many definite and indefinite equations (Diophantine, ancient Greece). During the Wei and Jin Dynasties from the 3rd century to the 4th century, there were ***2 1 propositions about the relationship between the three sides of a right triangle (China, Zhao Shuang). During the Wei and Jin Dynasties from the 3rd century to the 4th century, he invented the secant technique and got π = 3. 14 16 (China, Liu Hui). During the Wei and Jin Dynasties from the 3rd century to the 4th century, the method of calculating the distance and height of islands was discussed in the book "Calculation of Islands" (China Liu Hui). In the 4th century, the geometric work Mathematical Integration came out, which is a manual for studying ancient Greek mathematics (Pappus, ancient Greece). ◇40 1- 1000 ◇ In the fifth century, the approximate value of π was calculated to seven decimal places, more than a thousand years earlier than in the west (Zu Chongzhi, China). In the 5th century, he wrote a book about mathematics and astronomy, in which he discussed the solution of indefinite equations, metrology and trigonometry (Ayabata, India). In the 6th century, during the Six Dynasties in China, the ancestor's law was put forward: if the cross-sectional areas of two solid heights are equal, their volumes will be equal. It was not until the17th century that the same law was discovered in the west, which was called the cavalieri principle (China, Zuxuan). In the 6th century, "interpolation" was used to calculate the correct position of the sun and the moon in the calendar of the Sui Dynasty (China, Liu Zhuo). In the seventh century, definite and indefinite equations, quadrilateral, π, trapezoid and sequence were studied. The first general solution of ax+by=c (a, b and c are integers) is given (Brahmagupta, India). In the 7th century, the problem of finding the right root of cubic equation, which was put forward in large-scale earthwork, was solved in "Ji Gu Shu Jing" written by China and Wang Xiaotong in the Tang Dynasty. In the seventh century, the Tang Dynasty had Notes on Ten Calculations. "Ten Arithmetic Classics" refer to Zhou Xie, Jiu Zhang Arithmetic, Island Arithmetic Classics, Zhang Qiu Arithmetic Classics and Five Arithmetic Classics (China, Li,) and so on. ). In 727, an unequal interpolation formula was established in Yan Li during the Kaiyuan period of the Tang Dynasty (China, monk and his party). In the ninth century, the Indian counting algorithm came out, which made western Europe familiar with the decimal system (Arabic, Arabic submodule). ◇1001-1500 ◇1086-1093, and in the Song Dynasty, Meng Qian Bitan put forward "gap product" and "meeting circle", which started the research on higher-order arithmetic progression. 1 1 solved the root of the equation x2n+axn=b for the first time in the century (Al Karhi, Arabia). 1 1 Century completed a book on Algebra (Kayam, Arabic) and systematically studied cubic equations. 1 1 century solved the "Haisam" problem, that is, two straight lines on the circular plane should intersect at a point on the circumference and form an equal angle with the normal of that point (Egyptian, Al Haissam). 1 1 In the middle of the century, in the Nine Chapters of the Yellow Emperor's Arithmetic Fine Grass in the Song Dynasty, a method of "increasing, multiplying and opening" was created to open any higher power, and a binomial theorem coefficient table was listed, which was an early discovery of modern combinatorial mathematics. The so-called "Yang Hui Triangle" refers to this method (China, Jia Xian). /kloc-in the 0/2nd century, the book "Rilawati" was an important work on arithmetic and calculation in the East (Garo, Mais, India). 1202, Calculation Book was published, and Indo-Arabic notation was introduced to the west (Fibonacci, Italy). 1220 published the book Geometry Exercise, which introduced many examples that were not found in Arabic materials (Fibonacci, Italy). 1247, eighteen volumes of "Shu Shu Jiu Zhang" in Song Dynasty popularized the method of "increasing, multiplying and opening". The solution of congruence formula proposed in the book is more than 570 years earlier than that in the west (China, Qin). During the period of 1248, The Sea Mirror, a 12-volume edition of the Song Dynasty, was the first book to systematically discuss "Tianshu" (China, Li Zhi). 126 1 year, detailed explanation of nine chapters algorithm was published in Song Dynasty, and the sum of several high-order arithmetic progression was obtained by "piling" (China, Yang Hui). 1274, the Song Dynasty published the book Multiplication, Division and Change, which described the agile method of "nine returns" and introduced various calculation methods of multiplication and division (China, Yang Hui). 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. 1303, the Yuan Dynasty published "Siyuan Jade Sword" in three volumes, which upgraded Tianyuan Book to Siyuan Book (China, Zhu Shijie). 1464 In On Various Triangles (published in 1533), trigonometry (J. Miller, Germany) was systematically summarized. 1494 published Arithmetic Integral, which reflected the known knowledge about arithmetic, algebra and trigonometry at that time (Pachouri, Italy). ◇1501-1600 ◇1545, cardano published Ferro's formula for finding the general algebraic solution of cubic equation in Dafa (Italian, cardano, Ferro). 1550─ 1572 published Algebra, in which imaginary numbers were introduced, which completely solved the algebraic problem of cubic equations (Bombali, Italy). Around 159 1 year, a universal symbol appeared in Wonderful Algebra, which used letters to represent numerical coefficients, which promoted the general discussion of algebraic problems (Veda, Germany). 1596─ 16 13 completed fifteen decimal tables of six trigonometric functions with an interval of 10 second (Otto, Pittis, Germany). ◇1601-1650 ◇1614 years, formulated logarithm (Naipur, UK). 16 15 published "Solid Geometry of Barrels" to study the volume of conical rotating bodies (Kepler, Germany). 1635, published The Geometry of the Essential Continuum, in which the infinitesimal quantity was avoided and the simple form of calculus was calculated in an unmeasurable way (cavalieri, Italy). 1637, geometry publishing, analytic geometry formulation. Introducing variables into mathematics has become a "turning point in mathematics". "With variables, motion enters mathematics; with variables, dialectics enters mathematics; with variables, differentiation and integration immediately become necessary" (Descartes, France). 1638 Solving minimax problems by differential method (Fermat, France). 1638, he published "On Mathematical Proof of Two New Sciences", studied the relationship between distance, velocity and acceleration, and put forward the concept of infinite set, which was considered as an important scientific achievement of Galileo. 1639 published the draft of "trying to study what happens when a cone intersects a plane", which is the early work of modern projective geometry (De Shag, France). 164 1 year, the "Pascal, Blaise's theorem" about the hexagon inscribed in a cone was discovered (Pascal, Blaise). 1649, Pascal, Blaise calculator came out, which is the pioneer of modern computer (Pascal, Blaise). ◇1651-1700 ◇1654, studied the basics of probability theory (Pascal, Blaise, France, Fermat). 1655, arithmetica infinitorum was published, and algebra was extended to analysis for the first time (Varis, England). In 1657, he published an early paper on probability theory, on calculus of probability games (Huygens, Netherlands). 1658, The General Theory of Cycloids was published, and "Cycloids" were comprehensively studied (Pascal, Blaise, France). 1665- 1676 Newton (1665- 1666) formulated calculus before Leibniz (1673- 1676)./kloc 1670 put forward Fermat's last theorem, which predicted that if x, y, z and n are integers, then xn+yn = Zn, which is impossible when n > 2 (Fermat, France). 1673, the oscillating clock was published, in which the evolute line and evolute line of plane curve were studied (Huygens, Netherlands). 1684, he published a book about differential method, a new method of minimax and tangent (Leibniz, Germany). 1686, he published a book on integration methods (Leibniz, Germany). 169 1 year, the publication of elementary differential calculus promoted the application and research of calculus in physical mechanics (Switzerland, J. Bernoulli). 1696 invented the "Robida rule" for finding the limit of infinitives (Robida, France). 1697 solves some variational problems and finds the steepest descent line and geodesic line (J. Bernoulli, Switzerland). ◇1701-1750 ◇1704, published Counting Cubic Curves, Finding the Area and Length of Curves with Infinite Series, and Flowing Method (Newton, UK). 17 1 1 year published "Analysis of Using Series and Flow Number" (Newton, England). 17 13 years, the first book on probability theory "guessing" was published (Switzerland, Ya Bernoulli). 17 15, Incremental Method and Others (Bu Taylor, UK). 173 1 published the book "research on hyperbolic curves", which was the first attempt to study spatial analytic geometry and differential geometry (Crelo, France). 1733 normal probability curve was found (Demu Afer, UK). 1734, with the subtitle "to mathematicians who don't believe in God", Becker published "Analytical Scholars", which attacked Newton's "Flow Method" and caused the so-called second mathematical crisis (Becker, England). 1736 published the method of flow number and infinite series (Newton, England). 1736 published the Theory of Mechanics or Analytic Description of Motion, which is the first book to develop Newton particle dynamics by analytical method (Euler, Switzerland). 1742 introduces the power series expansion of functions (Kraulin, UK). In 1744, the Euler equation of variational method is derived, and some Swiss (Euler) surfaces are found. 1747, the theory of partial differential equations (French, da Lamber, etc. ). 1748, The Outline of Infinite Analysis was published, which is one of Euler's major works (Euler, Switzerland). ◇1751-1800◇1755-1774 published three volumes of differential calculus and integral calculus. The book includes the theory of differential equations and some special functions (Euler, Switzerland). From 1760─ 176 1 year, the variational method and its application in mechanics were systematically studied (Lagrange, France). 1767 discovered the real root separation method of algebraic equation and the method of finding its approximation (Lagrange, France). 1770─ 177 1 year to solve algebraic equations with permutation groups, which is the beginning of group theory (Lagrange, France). 1772 gives the initial special solution of three-body (Lagrange, method). 1788, analytical mechanics was published, and the newly developed analytical methods were applied to particle and rigid body mechanics (Lagrange, France). 1794, The Outline of Geometry, a textbook for elementary geometry, was widely circulated (Legendre, France). 1794, based on the measurement error, the least square method was proposed and published in 1809 (Gauss, Germany). 1797 published analytic function theory, and established differential calculus without limit concept by algebraic method (Lagrange, France). 1799, descriptive geometry was founded and widely used in engineering technology (gaspard monge). 1799 proves a basic theorem of algebra: algebraic equations with real coefficients must have roots (Gauss, Germany). ◇1801-1850 ◇180/year, published arithmetic research and initiated modern number theory (Gauss, Germany). 1809, the first book of differential geometry, The Application of Analysis in Geometry, was published (gaspard monge, France). 18 12, published in analytic probability theory, is a pioneer of modern probability theory (Laplace, France). 18 16 years, non-euclidean geometry was discovered but not published (Gauss, Germany). 182 1 year published "Analysis Course", strictly defined the continuity, derivative and integral of functions with limits, and studied the convergence of infinite series (Cauchy, France). 1822 systematically studies the invariance of geometric figures under projection transformation, and establishes projective geometry (French, Poncelet). 1822 studied heat conduction and invented Fourier series to solve boundary value problems of partial differential equations, which had great influence on theory and application (France, Fourier). In 1824, it is proved that it is impossible to understand the quintic equation with roots (Abel, Norway). 1825, invented Cauchy integral theorem about complex variable function, and used it to find some definite integral values commonly used in physics and mathematics (Cauchy, France). 1826 found that the sum of series of continuous functions is not a continuous function (Abel, Norway). 1826 changed the parallel axiom in Euclidean geometry and put forward the theory of non-Euclidean geometry (Russia, Lobachevsky, Hungary, Boyo). 1827- 1829, established the theory of elliptic integral and elliptic function, which has applications in physics and mechanics (German, Jacobian, Norwegian, Abel, French, Legendre). 1827 established the system theory of surfaces in differential geometry (Gauss, Germany). 1827 published gravity center calculus and introduced homogeneous coordinates for the first time (mebius, Germany). In 1830, an example of a continuous so-called "ill-conditioned" function without derivative is given (Porzano, Czech Republic). 1830 established group theory in the study of whether algebraic equations can be solved by roots (Galois, France). 183 1 year discovers the convergence theorem of power series of analytic functions (Cauchy, France). 183 1 year, the complex algebra was established, and the complex numbers were represented by points on the plane, which broke the mystery of complex numbers (Germany and Gaussian). 1835 put forward a method to determine the position of real roots of algebraic equations (Sturm, France). In 1836, the existence of solutions of differential equations with analytic coefficients is proved (Cauchy, France). In 1836, it is proved that the graph enclosing the largest area in all closed curves with known perimeters must be a circle (Steiner, Switzerland). 1837 gave a convergence theorem of trigonometric series for the first time (Dirichlet, Germany). 1840 applied analytic function to number theory and deduced "Dirichlet" series (Dirichlet, Germany). 184 1 year to establish the system theory of determinant (Jacobi, Germany). 1844, he studied multivariable algebraic systems and put forward the concept of multidimensional space for the first time (grassmann, Germany). In 1846, Jacobian (Germany) is proposed to solve the eigenvalue problem of symmetric matrices. 1847, Boolean algebra was founded, which has great application to later electronic computer design (Boolean, UK). 1848 studied the factorization of various number fields, and introduced the ideal number (Kumor, Germany). 1848 discovered an important concept of function limit-uniform convergence, but it was not strictly expressed (Stokes, UK). 1850 gives the definition of "Riemann integral" and puts forward the concept of function integrability (Riemann, Germany). ◇1851-1900 ◇185/year, put forward the principle of * * shape mapping, which has been widely used in mechanics and engineering technology, but has not been proved (Riemann, Germany) 1854 established a wider class of non-Euclidean geometry-Riemann geometry, and put forward the concept of multidimensional topological manifold (Riemann, Germany). The function approximation theory is established, and the complex function is approximated by elementary function. Since the 20th century, due to the application of electronic computers, the theory of function approximation has made great progress (Chebyshev, Russia). 1856 established the ε-δ method in limit theory and the concept of uniform convergence (Wilstras, Germany). Riemannian surfaces are discussed in detail in 1857, and multivalued functions are regarded as single-valued functions on Riemannian surfaces (Riemann, Germany). 1868 introduced some new concepts in analytic geometry, and proposed that straight lines and planes can be used as basic spatial elements (Pluck, Germany). In 1870, Lie groups were discovered and used to discuss the quadrature problem of differential equations (Norway, Li). The axiomatic structure of group theory is given, which is the starting point of later research on abstract groups (Kronig, Germany). 1872, mathematical analysis is "arithmetic", that is, real numbers are defined by the set of rational numbers (German, Detkin, Cantor, external ear Strass). Published the "Herun Root Plan", regarding every geometry as an invariant theory of a special transformation group (Klein, Germany). 1873, which proves that π is a transcendental number (Hermite, France). 1876, the analytic function theory was published, and the complex variable function theory was established on the basis of power series (Wilstrass, Germany). In 188 1- 1884, vector analysis (Gibbs, USA) is formulated. 188 1- 1886 published the paper "Integral Curve Determined by Differential Equations" continuously, and initiated the qualitative theory of differential equations (Poincare, France). In 1882, the expression of operational differential product is a simple method to solve some differential equations, which is often used in engineering (Havishay, UK). 1883 established the set theory and developed the theory of out-of-tolerance cardinality (Cantor, Germany). 1884 published The Basis of Number Theory, which is the origin of quantifier theory in mathematical logic (flaig, Germany). 1887- 1896 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 (Dalbet, Germany). Method. Then it is applied to electronic computers. 190 1 year, Dirichlet principle was strictly proved, which initiated the direct method of variational method and had many applications in engineering and technical calculation (Hilbert, Germany). 1907, proved a basic principle of the theory of complex variable function-Riemann * * * shape mapping theorem (Cobay, Germany). Oppose the use of law of excluded middle in mathematics and put forward intuitive mathematics (Homer, Brouwer, Lu). 1908, Formation of Point Set Topology (Simfries, Germany). Put forward the axiomatic system of set theory (Zemello, Germany). 1909, which solved the famous Hualin problem in number theory (Hilbert, Germany). 19 10 years, summed up the research on various algebraic systems such as groups, algebras and fields at the end of 19 and the beginning of the 20th century, and founded modern abstract algebra (Steinitz, Germany). He discovered the fixed point principle, and later discovered the dimension theorem and simplex approximation, which made algebraic topology a systematic theory (Dutch-American, Lu Brouwer). 1910-1913 years, he published Principles of Mathematics, trying to reduce mathematics to formal logic, which is the representative work of modern logicism (Britain, Bess, Whitehead). 19 13, E. Gaden 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, Hausdorff of Germany put forward the axiomatic system of topological space, which laid the foundation of general topology. 19 15 years, Swiss-born German-American Einstein and German Carl Schwartz applied Riemann geometry to the general theory of relativity and solved the spherically symmetric field equation, so that the motion of Mercury's perihelion can be calculated. 19 18, Hatay and Li Du wute in Britain applied the method of complex variable function theory to study number theory and established 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, Haenszel established the P-adic number theory, which is very useful 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, French E. Gardens put forward the differential geometry of general connection, which unified Klein's and Riemann's geometric views and was the beginning of the concept of fiber bundle. 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, Nath of Germany 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.