Gott's friend William Leibniz (1646- 17 16) is the most important mathematician, physicist and philosopher in Germany at the turn of 17 and 18 centuries, and he is a rare scientific genius in the world. He read widely and dabbled in encyclopedias, making indelible contributions to enriching the treasure house of human scientific knowledge.
I. Life story
Leibniz was born in a scholarly family in Leipzig, eastern Germany. His father is a professor of moral philosophy at Leipzig University, and his mother was born in a professor's family. Leibniz's father died when he was only 6 years old, leaving him a rich collection of books. Leibniz got extensive contact with ancient Greek and Roman culture and read the works of many famous scholars, thus gaining a solid cultural foundation and clear academic goals. /kloc-He entered the University of Leipzig to study law at the age of 0/5. As soon as he entered the school, he took a standard humanities course in his sophomore year. He also extensively read the works of Bacon, Kepler, Galileo and others, and deeply thought and evaluated their works. After listening to Euclid's "Elements of Geometry", Leibniz became interested in mathematics. /kloc-at the age of 0/7, he studied mathematics for a short time at the University of Jena and obtained a master's degree in philosophy.
At the age of 20, Leibniz transferred to Altdorf University. This year, he published his first mathematical paper "On the Art of Combination". This is an article about mathematical logic, and its basic idea is to reduce the theoretical truth argument to a calculation result. Although this paper is not mature enough, it shines with innovative wisdom and mathematical talent. Leibniz joined the diplomatic community after receiving his Ph.D. from Altdorf University. Since 167 1, he has developed extensive contacts with the outside world through diplomatic activities, especially communication has become the main way for him to obtain outside information and exchange ideas with people. During his visit to Paris, Leibniz was deeply inspired by Pascal's deeds and determined to study advanced mathematics, and studied the works of Descartes, Fermat, Pascal and others. 1673, Leibniz was recommended as a member of the Royal Society. At this time, his interest obviously turned to mathematics and natural science, and he began to study infinitesimal algorithms, independently established the basic concepts and algorithms of calculus, and laid the foundation of calculus together with Newton. 1676 went to the Duke of Hanover's house as a legal adviser and librarian. 1700 was elected as an academician of the Paris Academy of Sciences, which contributed to the establishment of the Berlin Academy of Sciences and served as the first president.
1716165438+10/0/4, Leibniz died in hanover at the age of 70.
Second, the original calculus
/kloc-in the second half of the 0/7th century, European science and technology developed rapidly. Due to the improvement of productivity and the urgent needs of all aspects of society, through the efforts of scientists from all over the world and the accumulation of history, calculus theory based on function and limit concept came into being. The idea of calculus can be traced back to the method of calculating area and volume proposed by Archimedes and others in Greece. Newton founded calculus in 1665, and Leibniz also published works on calculus in 1673~ 1676. In the past, differential and integral were studied as two mathematical operations and two mathematical problems respectively. Cavalieri, Barrow, Wallis and others have obtained a series of important results of finding area (integral) and tangent slope (derivative), but these results are isolated and incoherent. Only Leibniz and Newton really communicated integral and differential, and clearly found the internal direct relationship between them: differential and integral are two reciprocal operations. And this is the key to the establishment of calculus. Only by establishing this basic relationship can we establish systematic calculus. And from the differential and quadrature formulas of various functions, the algorithm program of * * * is summarized, which makes the calculus method universal and develops into a symbolic calculus algorithm. Therefore, calculus "was mostly done by Newton and Leibniz, not invented by them" (Engels: Dialectics of Nature).
However, there has been a heated debate in the field of mathematics about the order of the creation of calculus. In fact, Newton's research on calculus was earlier than Leibniz's, but Leibniz's results were published earlier than Newton's. Leibniz's paper "Finding a Wonderful Computing Type of Minimax" published in Teacher's Magazine on June 1684+00 is considered as the earliest published calculus document in the history of mathematics. Newton also wrote in the first and second editions of Mathematical Principles of Natural Philosophy published in 1687: "Ten years ago, in my correspondence with the most outstanding geometricians G and W Leibniz, I indicated that I already knew the method of determining the maximum and minimum, tangent method and so on, but I concealed this method in my correspondence ... The most outstanding scientists wrote back. He also described his method, which is almost no different from mine, except for his wording and symbols. " (But in the third edition and later editions, this passage was deleted. So it was later recognized that Newton and Leibniz created calculus independently. Newton started from physics and studied calculus by set method. His application is more combined with kinematics, and his accomplishments are higher than Leibniz's. Leibniz, on the other hand, started from geometric problems, introduced the concept of calculus by analytical method, and got an algorithm, which was more rigorous and systematic than Newton's algorithm. Leibniz realized that good mathematical symbols can save thinking labor, and the skill of using symbols is one of the keys to the success of mathematics. So he invented a set of applicable symbol systems, such as introducing dx to represent the differential of X, ∫ to represent the integral, dnx to represent the n-order differential and so on. These symbols further promoted the development of calculus. 17 13, Leibniz published the article "History and Origin of Calculus", summed up his own thought of establishing calculus, and expounded the independence of his own achievements.
Third, many achievements in advanced mathematics.
Leibniz has made great achievements in mathematics, and his research and achievements have penetrated into many fields of higher mathematics. His series of important mathematical theories laid the foundation for later mathematical theories.
Leibniz once discussed the properties of negative numbers and complex numbers, and concluded that the logarithm of complex numbers does not exist, and the sum of * * * conjugate complex numbers is a real number. In later research, Leibniz proved that his conclusion was correct. He also studied linear equations, discussed the elimination method in theory, introduced the concept of determinant for the first time, and put forward some theories of determinant. In addition, Leibniz also founded the basic concept of symbolic logic, and invented computers and binary systems that can perform addition, subtraction, multiplication, division and square root operations, which laid a solid foundation for the modern development of computers.
Fourth, the fruitful results of physics.
Leibniz's achievements in physics are also extraordinary. He published the "New Hypothesis of Physics", and put forward concrete and abstract principles of motion, arguing that a moving object, no matter how small, will move with a part of an object in a completely static state. He also seriously discussed the principle of conservation of momentum proposed by Descartes, put forward the rudiment of the principle of conservation of energy, and published a brief proof of Descartes and others' obvious mistakes in the laws of nature in Teacher's Magazine, put forward the problem of the quantity of motion, proved that momentum cannot be used as the unit of measurement of motion, and introduced the concept of kinetic energy, which was considered as a universal physical principle for the first time. He also fully proved that perpetual motion machine is impossible. He also opposed Newton's absolute view of time and space, arguing that "there is no space without matter, and space itself is not an absolute reality." The difference between space and matter is just like the difference between time and movement, but although these things are different, they are inseparable. " In optics, Leibniz has also made some achievements. He deduced the law of refraction by using the extreme value method in calculus, and tried to explain the basic laws of optics by using the extreme value method. It can be said that Leibniz's research on physics has been moving towards the goal of establishing an axiomatic system similar to Euclidean geometry for physics.
Verb (abbreviation of verb) is an advocate of cultural exchange between China and the West.
Leibniz attached great importance to China's scientific, cultural and philosophical thoughts, and was the first German to study China culture and China philosophy. He learned a lot about China from Grimal Di, a Jesuit missionary in China, including sericulture, textile, papermaking, printing and dyeing, metallurgy and minerals, astronomy and geography, mathematics and writing, and edited and published these materials. He believes that a new relationship should be established between China and the West. Leibniz wrote in the introduction of China: "The greatest culture and the most developed civilization of all mankind seem to gather at the two ends of our continent today, that is, Europe and Eastern Europe-China on the other side of the globe." "Compared with Europe, China, an ancient civilization, has a similar area and a population of more than." "We are neck and neck in our daily life and our skills in dealing with nature. We all have the skills to benefit each other through mutual communication. Obviously, we should be slightly better at careful thinking and rational thinking, but "in the philosophy of time, that is, in the ethics of life and human reality and the theory of governing the country, we are really dwarfed." Here, Leibniz not only shows the spirit of being open-minded and eager to learn without the color of "Eurocentrism", but also depicts the grand blueprint for the two-way exchange between Chinese and Western cultures, which has effectively promoted the in-depth development of this exchange. People in the East and the West should learn from each other, learn from each other's strengths and make progress together.
Leibniz devoted his life to promoting cultural exchanges between China and the West, which had a wide and far-reaching influence. He is open-minded and eager to learn, treats China culture equally, and his spirit of not containing the prejudice of Eurocentrism is particularly commendable, which is worthy of eternal admiration and imitation by future generations.