Famous saying

"I think, therefore I am."

-Descartes

"The turning point in mathematics is Descartes' variable. With variable, movement enters mathematics, with variable, dialectics enters mathematics. It is necessary to differentiate and integrate immediately. "

—— Introduction to Engels

On March 13th, 1596, René Descartes' cry came to the world in Toulon, on the Hilettani Peninsula in western France. Three days later, his mother died suddenly, and Descartes, who had lost his mother since childhood, was always weak and sick. Once sick, the young Descartes' life almost died, and under the careful care of his loving father, he turned the corner. René Descartes' name "René" means "rebirth" in French.

Descartes showed that he was diligent in thinking since he was a child. He liked to get to the bottom of many things and never blindly accepted other people's opinions. At home, the clever and articulate nanny was asked by the little Descartes who kept asking questions. At school, Descartes often asked many questions that his teachers had never thought of. Eight-year-old Descartes was sent to school by his father. Because Descartes' physique is much weaker than that of children of the same age, the principal authorized him to lie in his room and rest without going to class if he felt unwell. However, Descartes did not take this special care to sleep lazily, but closed his eyes slightly, but his brain kept speeding up the memory of what the teacher taught and what he had read, and asked questions, and then answered them with his own knowledge. There are always books on philosophy, mathematics, astronomy and history piled up beside his pillow, and Descartes' mathematical thought was conceived in the quiet meditation in his early years.

in p>1616, Rene Descartes received a doctor's degree in law from the University of Boaeton, and later became an officer in the Netherlands. One day, Beckman, who was quite famous at that time, posted a math problem on the wall and offered a reward for the answer. Descartes asked someone to help translate the title from Dutch into French. At that time, Beckman took a careless look at the young officer with a full face of beard. He never dreamed that Descartes handed in the correct answer two days later, and Descartes came to the fore. The adventure made the two mathematical geniuses become very close friends and became friends who discussed mathematics and science together. This success enabled Descartes to see his mathematical talent, which further aroused his research enthusiasm.

Descartes thinks that the essence of science is mathematics. He said, "I am especially happy with the certainty and clarity of mathematical reasoning." He emphasized that the purpose of science is to "benefit mankind" and make people become "masters and rulers" of nature.

Since Euclid's Elements of Geometry came out, people have always confined algebra to the study of numbers and their relationships, and geometry to the study of positions and figures. The separation of algebra and geometry lasted for thousands of years, just as two high mountains were divided by an abyss. The science that connects algebra and geometry and closely links "number" and "shape" is coordinate geometry founded by Descartes. The basic idea of coordinate geometry (later called analytic geometry) is to establish a coordinate system on a plane, which is composed of two orthogonal straight lines with marked direction and length units. Because the coordinate system is determined, any point on the plane can be represented by a pair of real numbers, and vice versa. In this way, the study of the relationship between figure and position can be transformed into the study of quantitative relationship and calculation through curve equation. From then on, the algebraic problem has a geometric intuitive explanation, and the geometric intuitive image is conducive to discovering its mathematical description. How did Descartes produce the idea of coordinate geometry? It is said that in the summer of 1619, Descartes went to the hospital because of illness. At noon, when he was lying in his hospital bed, he was thinking hard about a math problem and couldn't figure it out. Suddenly, he found a fly flying from one place to another on the ceiling. At that time, the ceiling was inlaid with wooden strips into a square figure. Descartes found that to tell the position of the fly on the ceiling, it is only necessary to tell which row and column the square where the fly is located is on the ceiling. When a fly lands on the square in the fourth row and fifth column, he can use (4,5) to represent this position ... So he thinks that this similar method can be used to describe the position of a point on the plane. He jumped off the bed happily and called "I found it, I found it", but accidentally spilled the chess on the quilt all over the floor. When his eyes fell on the chessboard, he patted his thigh excitedly: "Yes, yes, this is the picture". It is precisely because of Descartes' perseverance, hard-working spirit and determination to devote himself to science that he initiated a new era of mathematics and changed the historical process of science. It can be said that the rapid development of mathematics after the 17th century is largely due to the establishment of coordinate geometry.

In his Geometry, the idea of variables and functions first appeared. Descartes' so-called variables refer to line segments with varying lengths and constant directions, and also refer to numerical variables that continuously pass through all points on the coordinate axis. It is these two forms of variables that make Descartes try to create a science in which geometry and algebra permeate each other. Descartes' achievement is to unify the two research objects "shape" and "number" in mathematics, and to make them work in the future. He completed an epoch-making change in the history of mathematics. Engels spoke highly of this: "The turning point in mathematics is Descartes' variables. With variables, movement enters mathematics, with variables, dialectics enters mathematics, and with variables, differentiation and integration immediately become necessary." It should be pointed out that Descartes' coordinate system is incomplete, and he has not introduced the second coordinate axis. That is, the Y-axis. In addition, Descartes did not consider the negative value of the abscissa.

Descartes improved the symbols used by Veda. He used the first letters of the alphabet to represent the known number, while the last letters to represent the unknown number. This representation has been used to this day. He also considered the high-order parabola () and gave a rather ingenious method to tangent the cycloid.

Descartes' philosophical thought was highly praised by many people. Hegel called him "the father of modern philosophy". He was the first person to liberate philosophical thoughts from the shackles of traditional scholasticism and the founder of rationalism.

Under the influence of Beckman's "principle of conservation of motion", Descartes started to study physics. In the book Principles of Philosophy published in 1644, it made up for Galileo's shortcomings. He also thought that besides the law of the conservation of exercise, there should be two second-order laws: the first law is that the state of any matter particle, including its size, shape, position and motion, will not change without external action. The second law is that if an object is in motion, it will continue to move at the same speed and in the same straight line direction without stopping or deviating from the original direction if there is no other reason. Descartes first realized that the law of inertia was the key to solving mechanical problems and established it as a principle. This had a profound influence on Newton's comprehensive work later. In October, 1649, René Descartes came to Stockholm, Sweden, at the invitation of Christina, queen christina, to teach philosophy and mathematics to the 19-year-old girl. Unfortunately, Descartes fell ill because of her inadaptability to the Queen's living habits and the threat of severe winter. On February 11th, 165, the giant of science passed away.

Descartes died of pneumonia. Academics under the control of the church were very indifferent to Descartes' death, and only a few friends gave him a funeral. With the expansion of Descartes' influence on mathematics and philosophy, the French government transported his ashes back to the celebrity cemetery in Paris 18 years after Descartes' death. When commenting on Descartes' return to his native France, the German mathematician Jacques said humorously, "Possession of the ashes of great men, It is usually more convenient to possess themselves than when they were alive. "In 1799, his ashes were placed in the History Museum, and in 1819, they were moved into the Sacred Heart Hall of Saint-Germain. The tombstone reads: Descartes, the first person who fought for and guaranteed rational rights since the European Renaissance.