Reading Notes in Mathematicians' Eyes
Mathematicians' eyes are not about the skills to solve a certain kind of mathematical problems. It tells readers the ideas and methods of thinking about mathematical problems, focusing on helping readers improve their ability to solve mathematical problems in an all-round way. The mathematician's eyes is praised by experts at home and abroad as a world-advanced popular science masterpiece.
Mathematicians have different eyes from ordinary people: mathematicians may look at problems that ordinary people find complicated and difficult very simply; Ordinary people think it is quite simple, and mathematicians may think it is very complicated. Academician Zhang Jingzhong introduced how mathematicians found and drew extraordinary conclusions from these simple questions in a popular and vivid way. Mathematicians' eyes are not about the skills to solve a certain kind of mathematical problems. It tells readers the ideas and methods of thinking about mathematical problems, focusing on helping readers improve their ability to solve mathematical problems in an all-round way. The mathematician's eyes is praised by experts at home and abroad as a world-advanced popular science masterpiece.
In the preface of "Mathematical Circle", I wrote: Go, those mathematics distorted by the alienation of textbooks and test papers, forget that evil flower, and we will usher in a new hundred flowers garden. ..... carry forward the ideas and spirit of mathematics and mathematicians. The purpose is not to teach mathematics, but to change people's views on mathematics and mathematicians, so that mathematics can be integrated into popular culture and return to people's lives. With a little peace of literary appreciation, you can enjoy mathematics in a 360-degree state of mind, experience its interest and life, and feel the emotion and life behind the symbols. ..... In terms of number, mathematicians occupy a space with a measure of 0 at most among intellectuals. However, every progress in mathematics affects the foundation of the whole civilization. ..... "Who knows that there is a profound and consistent relationship between calculus and the dynastic principle of politics in Louis XIV, between the spatial perspective of western oil paintings and the victory of space with railways, telephones and long-distance weapons, and between para music and credit economy?" ..... When you find a small formula as sentimental as a poem, do you still have the heart to forget it?
Life in mathematics is simple. It has no smooth reasons and leaves no room for vague excuses.
Math life is also romantic. The imagination of artists is enviable, and that of mathematicians is even more. Hilbert said that if a mathematician becomes a novelist (there really is), we should not be surprised-because people lack enough imagination to become mathematicians, but they are enough to become novelists. Voltaire, who knows a little about mathematics, also thinks Archimedes has more imagination than Homer.
Mathematics is Ming Che's thinking. There are more people with mathematical thinking, and the space (especially those liars in scientific cloaks) is smaller. Infinite fantasy can find the most practical destination in mathematics.
Mathematics is a strange journey. ……
Mathematics is an art of pure beauty. There is no ugliness in the world of mathematics. In the eyes of mathematicians, their own formulas and symbols are like the king of Cyprus in Greek mythology, and from his statue, they see the life of his lover. In mathematics, in the logic that is harder than stone, there are mathematicians' pursuit of beauty, their temperament and their life.
Mathematics is a never-ending life. Learning mathematics feels like climbing a mountain, constantly climbing, in order to find a new peak. ……
The mathematical circle has no beginning and no end. No matter how you go, as long as you go far enough, you can always get somewhere.
I am deeply moved by this passionate and poetic language: mathematics, as a science, has made great contributions to the development of human civilization and should be cherished by all. This language is a plain statement of mathematics by an abnormal person, which makes me realize the pure and beautiful persistence under the rigorous coat of mathematics, and every sentence defends mathematics. As a math teacher who doesn't love math originally, and a person who knows little about math, I don't need to hide my ignorance about math. But I think, at least I have a reverence attitude towards mathematics, which led me into the mathematics circle. In this magical world, I gather every surprise and joy in my heart. One day, I will make students accept and like mathematics through my true feelings.
2.
Mathematical principles of natural philosophy.
Author: Sir isaac newton
Mathematical Principles of Natural Philosophy is a masterpiece of the first scientific revolution and is considered as the greatest scientific work ever. It has exerted great influence in the fields of physics, mathematics, astronomy and philosophy. In the way of writing, Newton followed the axiom model of ancient Greece and deduced propositions from definitions and laws (axioms). For specific problems (such as the movement of the moon), he compared the results of theoretical deduction with those of observation. The book is divided into five parts, the first is "definition", which gives the definitions of material quantity, time, space and centripetal force. The second part is "axiom or law of motion", including three famous laws of motion. The following contents are divided into three volumes. The titles of the first two volumes are the same, both of which are On the Motion of Objects. The first book studies the motion of objects in free space without resistance. Many propositions involve solving the motion state (orbit, speed, motion time, etc.). ) and the force determined by the motion state of the object. The second volume studies the motion, fluid mechanics and wave theory of objects with given resistance. The third volume of this book is entitled On the System of the Universe. Newton deduced the law of gravity from the first volume and the results of astronomical observation, and studied the shape of the earth, explained the tides of the ocean, explored the movement of the moon, and determined the orbit of the comet. The "rules of studying philosophy" and "general explanation" in this volume have great influence on philosophy and theology.
The mathematical principle of natural philosophy Newton's mathematical principle of natural philosophy is an epoch-making masterpiece in terms of the history of science and the whole history of human civilization. In the history of science, Mathematical Principles of Natural Philosophy is the first classic work of classical mechanics, and it is also the first complete scientific world view and scientific theoretical system mastered by human beings. Its influence covers all fields of classical natural science, and it has achieved fruitful results again and again in the following 300 years. From the inside of scientific research, Mathematical Principles of Natural Philosophy shows a model of modern scientific theoretical system, including theoretical system structure, research methods and attitudes, and how to deal with the relationship between man and nature. In addition, the mathematical principles of natural philosophy and the interaction between its authors and contemporary famous figures are also enduring topics in the study of the history of science and other academic history.
At that time, the Royal Society wanted to publish this book, but it couldn't come up with the right money. Hooke, director of the Royal Society, claimed that inverse square law, that is, gravity, was his first discovery. Out of anger, edmund halley suggested that Newton write this book, and he published Newton's book at his own expense. 1687 In July, the Latin version of Mathematical Principles of Natural Philosophy came out. The second edition was published in 17 13, and the third edition was published in 1725. Mott translated it into English on 1729, which is the popular English version now. Each edition was updated by Newton himself with a preface. There are many later versions, and the Chinese version is published in 193 1. The purpose of this book is to explore the natural forces from various moving phenomena, and then use these forces to explain various natural phenomena.
This book is divided into four parts. The opening and the first article introduce the three basic laws of motion and basic mechanical quantities of mechanics; The concept of mass was first put forward and defined by Newton, but Newton called it "the quantity of matter" at that time, and this name was later used by another physical quantity. In the second chapter, the motion of an object in a damping medium is discussed, and the formula that the resistance is proportional to the first and second squares of the velocity of the object is put forward. The elasticity and compressibility of gas and the speed of sound in air were also studied, which provided Newton with a stage to show his mathematical skills. The third topic is the cosmic system, which discusses the operation of planets, satellites and comets in the solar system and the generation of ocean tides, involving perturbation in many-body problems.
Newton did not claim to have built a system. Newton pointed out at the beginning of the preface to the first edition of Mathematical Principles of Natural Philosophy that he would "devote himself to the development of mathematics related to philosophy". This book is a combination of geometry and mechanics, a kind of "rational mechanics", and a kind of "science of accurately asking questions and demonstrating them", aiming at studying the movement produced by a certain force and the force needed for a certain movement. His task is to "study natural forces from dynamic phenomena, and then deduce other motion phenomena from these forces."
However, Newton actually built the most magnificent system in human history. What he said is mainly gravity, which is what we call gravity today, and the friction, resistance and tidal force of the ocean derived from gravity. Motion includes falling body, throwing body, rolling ball, simple pendulum and compound pendulum, fluid, planetary rotation and revolution, return point, orbital nutation and so on. In short, it includes, in other words, Newton explained all movements and phenomena from ground objects to celestial bodies with unified mechanical reasons.
Structurally, the mathematical principle of natural philosophy is a standard axiomatic system. Starting from the most basic definitions and axioms, it "deduces some general propositions in the first part and the second part". The first part, entitled "Motion of Objects", prepares the discussion of the whole book with mathematical tools, classifies various forms of motion, and examines the relationship between each form of motion and force in detail. The second part discusses "the motion of an object (in a blocked medium)", and further investigates the influence of various forms of resistance on the motion, and discusses various actual forces and motions on the ground. The third part "demonstrates their application to the cosmic system, deduces the gravitational force that makes objects tend to the sun and planets from astronomical phenomena with the propositions proved by the first two parts, and then calculates the movements of planets, comets, moons and oceans from these forces with other mathematical propositions". At the end of the book, Newton wrote a famous General Explanation, which focused on Newton's views on the fundamental reason of everything in the universe-gravity and the general reason why our universe is such a beautiful system, and his views on the existence and essence of God.
In terms of writing skills, Newton is a very attentive person. Although he established his own system according to Euclid's Elements of Geometry, he never forgot that his mission was to explain natural phenomena, and he was not lost in pure formal reasoning. He is an excellent mathematician and has a series of first-class inventions in mathematics, but he strictly regards mathematics as a tool and only leads readers to do a little math hiking when necessary. On the other hand, Newton never thought about pure philosophy at all. All the propositions in Mathematical Principles of Natural Philosophy come from the real world, either mathematics, astronomy or physics, that is, Newton understood natural philosophy. All the expositions in Mathematical Principles of Natural Philosophy are given in the form of propositions, and each proposition is proved or solved. All proofs and solutions are completely mathematical, and inferences will be added when necessary, and each inference has a proof or solution. Only when Newton thinks that a problem has special significance in philosophy, does he add notes to explain it or further popularize it.
Calculus, a mathematical method independently invented by Newton and Leibniz, runs through the book, but Newton called it "flow number", which is one of Newton's achievements. It occupies a very important position in the history of science, because it marks the establishment of the classical mechanical system.
Newton published three editions of Mathematical Principles of Natural Philosophy in 1687, 17 13 and 1726 respectively, all in Latin. The first English translation after Newton's death was translated from the third edition published in 1729 by Andrew Mott. 1802, the English version based on the first edition of Mathematical Principles of Natural Philosophy appeared. From 65438 to 0930, florian Kaio, an American scholar and historian of science, revised and published Mott's English version in modern English, which became the standard edition of Mathematical Principles of Natural Philosophy with the largest readership in the 20th century. In the early 1960s, Cohen, an American historian of science, cooperated with A 1exander Koyré, a French historian of science, and published a modern English version of Mathematical Principles of Natural Philosophy on the basis of the first English version translated by Mott.
In the history of science, Mathematical Principles of Natural Philosophy is the first classic work of classical mechanics, an epoch-making masterpiece, and the first complete scientific cosmology and scientific theoretical system mastered by human beings. Its influence covers all fields of classical natural science, and it has achieved fruitful results again and again in the next 300 years. As far as the history of human civilization is concerned, it has achieved the industrial revolution in Britain, induced the Enlightenment and the Great Revolution in France, and made direct and rich achievements in both social productive forces and social basic systems. So far, there is no second important scientific and academic theory that has made such great achievements.
The mathematical principle of natural philosophy has reached a theoretical height that is unprecedented and unprecedented. Einstein said, "It is impossible to replace Newton's concept of universal unity with an equally all-encompassing concept of unity. Without Newton's clear system, the gains we have made so far will be impossible. In fact, the problems discussed by Newton in Mathematical Principles of Natural Philosophy and the methods to deal with them are still taught by university mathematics majors, while the knowledge of physics, mathematics and astronomy learned by students of other majors has not reached the level of mathematical principles of natural philosophy in depth and breadth.
All these determine the eternal value of the book Mathematical Principles of Natural Philosophy. Although this book has been published for hundreds of years, its scientific spirit is immortal and worth reading!