Descartes Date of Birth: 1596~ 1650 Nationality: French works: On the World, Methodology, Metaphysical Meditation and Philosophical Principles, Geometric Life: Descartes is a famous French philosopher, mathematician, physicist and natural scientist. On March 3rd, Kloc-0/596 was born in a noble family in Toulon. When I was a child, I cut public school in Lafleur. Because I was weak, I was allowed to study in bed in the morning, and gradually developed the habit of loving peace and being good at thinking. Mei Sen, a close friend, was formed in school. 16 12 went to the university of poitiers in Paris to study law. Four years later, he was awarded a doctorate and became a lawyer. At that time, people with lofty ideals in French society were very popular, either in religion or in the military, which drove Descartes to join the army in the Netherlands in 16 18. During his service, he was still interested in mathematics. One day on vacation, he was attracted by a poster in Dutch when he was walking in the street, but because he didn't know Dutch, he asked people around him to translate it into Latin or French. It happens that this person is beekman, Dean of Dortmund College. After this translation, Descartes learned that this was a "challenge book" written by mathematicians at that time, and collected the answers to the above questions. Descartes found the answer in a few hours, which greatly admired Bi Ke. 162 1 year, Descartes left the army and returned to France, but it coincided with civil strife, so he traveled to Denmark, Germany, Italy and other places. It was not until 1625 that he returned to France to discuss mathematics with Mei Sen and others. He moved to the Netherlands from 65438 to 0628, and kept close contact with major European scholars through his mathematician father Mei Sen. In his spare time, he engaged in research in the fields of mathematics, astronomy, physics, chemistry and physiology. Almost all his works were completed in Holland. His main works have guiding philosophical principles; [Written in 1628] On the World Based on Copernicus Theory was completed in 1634, but it was not published because Galileo was persecuted by the church], and the methodology was published anonymously in Leiden on June 8, 2007, Metaphysical Meditation and Philosophical Principles [1644]. /kloc-in the winter of 0/649, he was invited to Stockholm to give a class to queen christina Christina. Finally, this mathematician, who is famous for creating analytic geometry, died of pneumonia in the local area on February 1650. Descartes had doubted and opposed the scholasticism that ruled the European ideological circle as early as his student days. Years of travel and scientific research, combined with contacts with people from all walks of life and constant self-reflection, made him firmly believe that he must abandon scholasticism, explore the correct thinking method and create a philosophy serving practice in order to become the master and ruler of nature. "He thinks that mathematics is the ideal and model of all other sciences, and puts forward methodology and epistemology based on mathematics and with deduction as the core. He became one of the founders of modern western philosophy and had a great influence on later philosophy, mathematics and natural science. In addition, he has been fighting against the church and other opposition forces to defend his theory. In addition, his Methodology (the earliest work) written in French in 1637 was accompanied by three short articles and a preface, namely Refractive Optics, Meteorology, Geometry and Methodology of Correctly Applying Reason and Pursuing Truth in Science. Among them, Geometry is a masterpiece, which established his position in the history of mathematics. This is also his only math paper. The Book of * * * is divided into three volumes, which analyzes the advantages and disadvantages of geometry and algebra, and expresses the necessity of seeking another method that contains both advantages and disadvantages. In the first book, he transformed geometric problems into algebraic problems and put forward a unified drawing method of geometric problems: using the concepts of unit line segment and square root of line segment, the line segment is connected with quantity, and the equation is established through the relationship between line segments. In the second volume, when he used this new method to solve the Pappus problem, he defined a point, and selected another straight line intersecting the point on the plane as the baseline. The three items were the X axis, the point and the Y axis, respectively, to form an oblique coordinate system. At this time, the position of any point on the plane can be uniquely represented by [x, y]. The Pappus problem is reduced to a binary quadratic indefinite equation. He pointed out that the number of equations has nothing to do with the choice of coordinate system, so curves can be classified according to the number of equations. In the third volume, he pointed out that an equation can have as many roots as its times, and put forward the flute rule: the maximum positive root number of an equation is equal to the number of times its coefficient changes sign; The maximum number of its negative roots (pseudo-roots) is equal to the number of times the symbol remains unchanged. Descartes also used A, B, C, ... to represent known quantities and X, Y, Z, ... to represent unknown quantities, so as to improve the symbol system created by Vedas. Geometry puts forward the main ideas and methods of analytic geometry, which marks the birth of analytic geometry. Descartes devoted his life to the study of knowledge groups, which brought rich achievements to the scientific treasure house of mankind and had a far-reaching impact on the research of later generations. Fermat Pierre de's date of birth: 160 1~ 1665 Nationality: French life: Fermat 16065438 was born in Dromana, southern France. He was educated in his hometown in his early years, and later entered the University of Toulouse to study law. After graduation, he worked as a lawyer and became a member of parliament in Toulouse from 163 1. During this period, he specialized in mathematics in his spare time, and often corresponded with Descartes, Mei Sen and other famous scholars to discuss mathematical problems. He has read a lot of books, is good at several languages and has mastered a lot of scientific knowledge. Although I paid close attention to mathematics when I was nearly 30 years old, I made great achievements. Finally, he died in castel on 1655. Because of his indifference and humility, he rarely published his works, and most of his achievements were only left in the blank of manuscripts, letters or books. His son compiled his manuscript into a book and published it in Toulouse on 1679. Fermat and Descartes were both the earliest mathematicians in the first half of17th century. In modern number theory, no one can match them before Euler a century later. He discovered the basic principles of analytic geometry independently of Descartes. Because the method of finding the tangent of a curve and its minimum value is considered as the pioneer of calculus. Through Pascal's correspondence, he became one of the co-founders of probability theory. 1629, he began to rewrite the long-lost ; & gt people soon found that it would be easy to study the trajectory by using algebra in geometry through coordinates. In optics, Fermat applied minimax method, revealing that the refraction law of light is consistent with his "shortest time principle". Suffering < < Arithmetic > > Influenced by this book, Fermat got many new results in number theory. One of the most outstanding results is that the prime number of 4n+ 1 can be uniquely expressed as the sum of two squares. Among Fermat's last theorem, there are two theorems called the great theorem and the small theorem respectively, and the former is also called the last theorem. This little theorem was put forward by Fermat in a letter to his friend Frannico. Its content is that if P is prime and a p is coprime, then A minus the power of A can be divisible by P. The great theorem is that if n2, the equation has no integer solution. Fermat wrote this theorem in the blank space of the book and found a wonderful proof method, but the blank space was not enough to write it down. Because of his great contributions in number theory, analytic geometry and probability theory, he was praised as "the king of amateur mathematicians" by later generations. Source: History of Mathematics-Development of Mathematical Thought (I) P296 and website: Gilles Personne de Roberval (www.mcjh.kl.edu.tw/usr/jks/jks.htm) Date of birth: 1602~ 1675 Nationality: French life: Robert is a French mathematician. Curve geometry has made great progress. From 65438 to 0632, he was a professor at the Institut de France in Paris. The method of measuring the surface area and volume of solid was studied. Robert often had scientific debates with mathematicians at that time, including Descartes. Robert summarized Archimedes' method of finding the tangent line on the spiral in his novel (although it was published as late as 1693 and has been recorded since 1634). Like Archimedes, Robert regards the curve as the trajectory of a moving point, which is influenced by two kinds of velocities, such as the object thrown from the muzzle and the horizontal velocity. Robert regards this composite vector as the tangent of the curve at point P; According to Torricelli's explanation, the Roberts method is based on a theorem asserted by Galileo: horizontal velocity and vertical velocity are independent of each other. The argument that the tangent is regarded as the synthetic velocity is far more complicated than that of the Greek era when the tangent was regarded as a straight line in contact with the curve. The former solved many problems that the latter could not. It plays a very important role in connecting pure geometry and dynamics. Before Galileo, pure geometry and dynamics were separated. In other words, this tangent view materialized the mathematical garden, because it defined the tangent with physical concepts. But there are many curves that have nothing to do with motion, so the tangent line is produced for no reason, and other methods are needed to find the tangent line. Source: History of Mathematics-Development of Mathematical Thought (1) P37 1