? Among the outsiders, some people brought Sumerian influence and knowledge to Egypt, where civilization also made great achievements. Because of papyrus, we know more about Egypt than Babylon. Egyptians made extensive contributions to mathematics. They completed four basic arithmetic operations, extended them to fractions, and found a method to find approximate square roots. They have mastered the knowledge of arithmetic series, geometric series, quadrature of three-dimensional figures, elementary trigonometric functions and quadratic equations. However, neither the Babylonians nor the Egyptians made patient and meticulous investigations on natural phenomena, nor did they have the ability to generalize and reason, so these ancient civilizations did not produce real science.
Although the Greeks inherited a lot of information from ancient culture, almost everyone admitted that the Ionian coast of the Aegean Sea was the origin of all science today. Babylonians and Egyptians never thought of seeking knowledge for the sake of knowledge itself, but it was this idea that prompted the "Greek scientific miracle", and the most amazing progress occurred in the field of mathematics, which laid a permanent foundation for its future development. The Ionian school headed by Thales brought geometry and other knowledge back to Greece from Egypt and Babylon, and put forward many propositions and basic principles. At the end of 6th century BC, due to the invasion of Persia, people fled to the west, and Italy and Sicily became new academic centers. The Pythagorean School, founded in southern Italy, turned mathematical research into a form of free education, and the whole mathematics became more abstract and divorced from the needs of economic life. The Pythagorean school had a great influence on the development of mathematics, which lasted for two centuries.
? After Persia was defeated by the Greek Coalition forces in 480 BC, Athens became the economic and cultural center of the world. At this time, philosophers with the purpose of educating people and spreading culture appeared, and their thoughts had a great influence on the development of geometric problems such as rulers and ruler drawing, among which Zhi Nuo's famous paradox about infinity was one. After the threat of Persian nomads was eliminated, the alliance between Athens and Sparta was replaced by suspicion and discord. The Peloponnesian War lasted until 404 BC, when Athens was forced to surrender. This period is the era of Socrates and Plato. Unlike Socrates, the teacher, who was obsessed with the country and ethics, Plato became interested in mathematics during his travels. Therefore, Plato's academy philosophy, which has a far-reaching influence on later generations, has also become a philosophy of mathematics. Aristotle, a great scholar and philosopher, was also a student of Plato's Academy. He made people understand the difference between axiom, postulate and definition. His works contain many important theorems. A large number of works left by Aristotle directly ruled all the theories of the later Renaissance, even though those wrong mechanical principles continued to16th century.
After Macedonia completely defeated Athens in 338 BC, Athens never recovered. Two years later, Alexander the Great, the new king of Macedonia, set out to conquer the world and established a huge and short-lived empire. In 332 BC, he founded the city of Alexandria by the Nile. Ptolemy, the later ruler of this city, was a student of Aristotle like Alexander the Great, and Alexander soon became a new economic and cultural center. Since then, Alexandria's position as an academic center has lasted for thousands of years, until it was looted by Arabs in 64 1 year.
? Among the scholars in Alexandria, three people decided the mathematical course in the following hundreds of years: Euclid, Archimedes and Apollonius. The Elements of Geometry written by Euclid in 320 BC is the cornerstone of European geometry. The axiomatic method used by Euclid later became a model of establishing any knowledge system and was regarded as a model of rigorous thinking that must be observed for two thousand years. Archimedes is called the greatest mathematician in ancient times. His discovery covers a wide range, such as giving many methods to find the center of gravity of geometric figures, including the center of gravity of the figure surrounded by parabola and its parallel chords, and finding the volume of ellipsoid and rotating projectile. Through continuous division, this has the embryonic form of integral calculation. Apollonius, a gifted geometer, wrote the book "Conic Curve", which completely captured the nature of conic curve and left little room for later generations to set foot in it.
After the first year of AD, although the study of mathematics in Alexandria continued, people's interest in this subject was gradually weakening. The golden age of Greek science is fading away, replaced by Roman culture, which is extremely practical and indifferent to the pursuit of wisdom, followed by the Middle Ages, which lasted 1000 years. This is a dark age, and the glory of Greek philosophers seems to be far away from this land. Both mathematics and other ideas are mostly in a state of stagnation or even decline. However, earth-shaking changes are slowly brewing, which will eventually bring complete light and revival.
Although the Renaissance is generally regarded as "the greatest and most progressive change that mankind has never experienced", as far as mathematics is concerned, the flame of wisdom constantly emerges and resists in the dark period. The Byzantine Empire in the East has always maintained an academic background and preserved many Greek academic works. After the rise of Arabs, they quickly developed a high degree of culture from the intersection of East and West, and Greek culture was thus preserved. After Christianity conquered Spain, Arabic culture was used in western Europe, and a large number of Greek works were translated into Latin. After China's compass was introduced to the west, the strong demand for improving navigation technology greatly affected the two basic sciences of astronomy and mathematics. However, people in the Middle Ages respected Aristotle's authoritative position so much that the knowledge of purely explaining historical documents appeared. This runs counter to the idea of natural science. In such an atmosphere, mathematics can only be barely maintained.
1453, Constantinople was captured by the Turks. The Byzantine Empire, which inherited Rome and Greece and lasted for thousands of years, collapsed. Many scholars took refuge in Italy with their works and were welcomed by medici family. The west can finally see the original Greek classics directly, and the whole western world has also unveiled that most famous prosperity period.
? Mathematics didn't fall behind in this comprehensive renaissance, and soon gained a leading position that has never been seen since the decline of Greek culture. Arithmetic, which was previously neglected, began to rise. The solutions of cubic and quartic equations have been obtained, and negative numbers and even imaginary numbers have been given their due status. Trigonometry began to appear as an independent discipline, but the fact that it belongs to the category of physics is very important to this paper: the silent 18 century mechanics finally began to attract people's attention. The Renaissance began in Italy and Germany, which were the most powerful countries at that time. The Hanseatic League still controlled the northern trade, while Florence and Venice were at the peak of prosperity. The importance of France did not appear until the end of 16, and it occupied a leading position for a century.
1600 may be the beginning of the most important century in the history of mathematics. Descartes was born four years ago, followed by Pascal and Fermat. These three people are destined to change the whole face of mathematics. In the16th century, most mathematics disciplines have made concrete progress, but the beginning of the new century indicates more spectacular development. The application of algebra in geometry made Descartes perfect analytic geometry, Pascal developed projective geometry, and the application of decimals and logarithms improved the calculation method. Fermat and others began to study number theory and probability theory, and introduced the ancient minimal partition method into geometry, which eventually led to the invention of calculus. Descartes and Fermat invented analytic geometry on the basis of Kepler and others. Cartesian geometry is a classic of analytic geometry. The earliest exploration of probability theory is attributed to Fermat and Pascal. After a long history, this research still attracts the attention of many scientists until now.
? With the steady progress of mathematics, mechanics has fallen behind. Although Archimedes pointed out the right direction, little progress has been made since 1800. But after 16, due to the appearance of machines, the study of mechanical principles finally began. Galileo, Descartes, Huygens and others greatly expanded this subject. However, in their hands, mechanics has reached such a height that it is almost impossible to make further progress without inventing new and more powerful methods, and the situation in mathematics at the same time is similar. Fortunately, this phenomenon did not delay for a long time, because Newton was born in 1642.
Calculus did not come into being suddenly without its predecessor, but was the crystallization of many scholars' long-term exploration. Archimedes determined the area of the graph by exhaustive method, from which we can clearly see the analysis principle of infinitesimal. After 2000, cavalieri resumed his exploration in this field, and after the popularization and perfection of Torricelli, Fermat, Huygens and Wallis, the form of summation in integral calculus was formed. Descartes and Fermat developed the problem of curve tangent after Archimedes' spiral tangent.
? Newton's law of universal gravitation and binomial theorem are great contributions, and his immortal working principle marks the establishment of classical mechanical system. The whole book runs through the concept of flow number, which is calculus. Newton's importance lies in that he put forward the basic concepts of calculus, such as variability, reciprocal differential and integral, and turned this method into a complete tool system. In Germany, Leibniz developed the principle of calculus. According to Leibniz's account, he invented calculus in 1674, and Newton claimed that he gradually attacked calculus in 1666. As a result, mathematicians in Britain and continental Europe parted ways, which is an unfortunate chapter in the history of science. In this debate, Leibniz's notation has been used to this day, and now it is recognized that Newton and Leibniz independently created calculus. The establishment of calculus marks a new era in the world. From the17th century, science began to transform the original Christian-centered culture into such a science-centered culture.
1640 After the British bourgeois revolution, Britain established a constitutional monarchy, and the world entered a period of modern history. The Kingdom of Prussia was founded in 170 1 year, the United States became independent in 1776, and the French Revolution took place in 1789. The decline of feudal system and the growth of capitalism were the central contents of this period, and Britain, Germany and France became the main destinations of mathematicians in this period. /kloc-in the second half of the 0/7th century, mathematics made amazing progress. Calculus is a powerful tool, but its foundation must be strictly checked. This is one of the main tasks in the next century. 18th century, the mainstream of mathematics is mathematical analysis developed from calculus. The development of mathematical analysis has deepened mechanics and celestial mechanics, and the latter has become the driving force for the development of mathematical analysis.
? From the mathematician's point of view,18th century is a "heroic era", with various heroes, including the famous Bernoulli family in the history of science; Euler, who made important contributions to almost every branch of mathematics; Cauchy, who gave calculus a clear and rigorous foundation; Lagrange,/kloc-the top mathematician in the 0/8th century; In addition, there are Taylor, maclaurin, Sterling, Langdon, Fourier and so on, who have made outstanding contributions to the development of calculus. Gaspard monge, Cano and Penceler pioneered modern geometry. Lagrange came to Berlin on 1766 at the invitation of frederick the great. In these 20 years, his works are vast, and his greatest work, Analytical Mechanics, was brewed. At that time, the revival of France had begun to take shape, and Paris once again became the center of mathematics education. Laplace, like Lagrange, is a master of analysis. He made amazing achievements in celestial mechanics. He wrote a book, Celestial Mechanics. As Napoleon's soldiers swept across Europe, this era was also one of the richest scientific achievements in French history.
At the end of 18, the greatest progress was made on the land of France. With the coming of19th century, Germany quickly jumped to the top. Gauss, Abel, Galois and others carried forward Fermat's contribution to algebra. Gauss is the greatest mathematician of this era and all times. He demanded more rigor in mathematics, and comprehensively developed all fields of pure mathematics and applied mathematics. Because of Gauss's various studies, mathematics has become more and more specialized and divorced from the needs of economic life, and scholars have begun to cultivate their interest in learning mathematics for the sake of mathematics.
? 1897 held the international congress of mathematicians, which opened the era of great development of pure mathematics in the 20th century. There are more and more branches of mathematics, and each branch needs experts to study. The last person who tried to set foot in the whole field was Poincare. At present, even if there is a second Gaussian, it is doubtful whether he can involve very few branches. Mathematics has developed to such a huge structure and plays a cornerstone role in various disciplines. Now we can say unequivocally that mathematics is the king of all sciences.
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