Mathematicians know that their inventions have not been systematically stated by Euclid's deduction, but they firmly believe that this is the truth. Their confidence comes partly from the physical correctness of their conclusions and partly from philosophy and theology. From the late17th century to the late18th century, Thomas Hobbes, Locke and Leibniz expounded the philosophical theme and established the harmonious unity of reason and nature. The performance of mathematical deduction in celestial mechanics is an evidence that people believe in the mathematical design of the universe. In the18th century, people also believed that some mathematical principles must be correct, such as the principle of minimum work asserted by Maupertuis and supported by Euler.
The early connection between science and theology made people believe that the world was designed according to mathematics. 16 and 17 century leaders not only believed in religion, but also looked for inspiration and belief in scientific work in religion. Copernicus and Kepler believed in Heliocentrism because they believed that God liked simple theories in mathematics. Descartes believes that our innate ideas (including mathematical axioms) are correct, because he believes that God will not deceive people, and denying the truth of mathematics means denying God. Newton thought the value of his work was to study God's work and support the apocalypse. Leibniz also believes that the universe is perfect, and rational thinking reveals its laws. In the18th century, people still believed that nature was designed according to mathematics, but abandoned the philosophical and religious basis. Pure mathematical and physical explanations weaken the foundation of the theory that the universe was designed by God. /kloc-in the 0 th and 7 th centuries, mathematicians also opposed religious forces. For example, Galileo said that the discussion of the Bible was a lie and meaningless, while Descartes advocated that the laws of nature remain unchanged, which implicitly limited the role of God. Although Newton believed in God, he believed that God's function was to make the world run as planned. With the development of mathematics, religion has less and less enlightenment and promotion to mathematics.
Although Lagrange accepted the minimum working principles of Maupertuis and Euler, he denied that there was anything metaphysical in them. People are more concerned about important physical results than God's design. Laplace completely abandoned the God or metaphysical foundation in mathematical physics. There is a famous story: Laplace gave Napoleon a copy of his Celestial Mechanics. Napoleon asked why there was no mention of the creator of the universe. Laplace replied, "I don't need this assumption." By the end of 18, metaphysics has become a derogatory term, and people also use this word to accuse what they don't understand. For example, gaspard monge's contemporary mathematicians did not understand his characteristic function theory, so they called it metaphysics.
The expansion of mathematical activities
18th century17th century The Academy of Sciences was established, and the periodicals run by the Academy became the official channels for publishing articles. 1785, the Paris Academy of Sciences was reorganized into one of the three branches under the French Academy.
Before 1800, German universities did not do research, but only provided two-year compulsory courses in humanities and specialized courses in law, theology and medicine. Mathematicians do research at the Berlin Academy of Sciences. But in 18 10, alexander von humboldt established the University of Berlin, and proposed that professors should talk about what they want to talk about, and students can learn what they like. Jacoby teaches elliptic functions from 65438 to 0826 in Koenigsberg, but this situation is rare, and many teachers still have to take regular classes. /kloc-In the 20th century, many universities were established in Germany and began to support professors engaged in research.
/kloc-French universities in the 0/8th century are not as good as German universities before the French Revolution. The new government decided to build a high-level university, and condorcet organized this work. 1794 set up a multidisciplinary technical school. Gaspard monge and Lagrange were the first mathematics professors, and the school trained students to become engineers or officers. The school's mathematics level is very high, and graduates can carry out mathematics research. 1808, the French government established higher normal schools to train teachers of humanities and natural sciences.
/kloc-in the 0/8th century, there was a great gap in the number of mathematical achievements among European countries, with France leading and Switzerland following. Although the Berlin Academy of Sciences funded Euler and Lagrange, German mathematics research is relatively inactive. The same is true in Britain. Only Taylor, Matthew Stewart (17 17- 1785) and maclaurin are pitifully few compared with 17th century. Because of the dispute between Newton and Leibniz, the British have been working on Newton's geometric methods, using Newton's symbols and even refusing to read and write with Leibniz's symbols. Oxford and Cambridge refused to accept Jews and non-Anglican believers, and English mathematics and astronomy died out around 18 15.
/kloc-In the first quarter of the 9th century, British mathematicians finally became interested in the work of calculus in continental Europe, and the Analytical Society was founded in Cambridge in 18 13. George Pique (179 1- 1858), John Herschel (1792- 18765438), Charles Babbage and others studied "d- ism" (Leibniz used it. 18 16, Babbage, Herschel and peacock translated and published Lacroix's first volume, The Tutorial. By about 1830, the British had kept up with the work in the mainland. Most of the analysis in Britain is mathematical physics, but Britain has also initiated several new work directions (algebraic invariant theory and formal logic)
Take a look forward
By the end of 18, mathematicians had started a new branch of mathematics, but the problem was very complicated and no universal solution was found, so mathematicians felt that it had come to an end. 178 1 year, Lagrange wrote to D'Alembert, saying that he felt that the mine of mathematics was almost finished, and it was more promising to engage in physical chemistry. Euler and D'Alembert also agree with Lagrange that there are no new bulls in the field of mathematics (Gauss: Don't prompt before going to school). As early as 1754, Diderot couldn't say that mathematics would be completed in a century, and everyone could only gnaw at the roots of Bernoulli, Maupertuis and Claire. When talking about the future of mathematics, Delabray (1749- 1822), Permanent Secretary of the Department of Mathematics and Physics of the French Academy, said that people are blocked by insurmountable difficulties in almost all branches, and it seems that everyone can only improve in details.
178 1 year, condorcet made a wise prediction, and gaspard monge's works left a deep impression on him. He believes that mathematicians are only the first step of the long March, and there are still many problems to promote the progress of mathematics in the future. Condorcet was right. In the19th century, mathematics expanded more than in the18th century. 1783, Euler and D'Alembert died. Laplace is 34 years old, Legendre is 3 1 year old, Fourier 15 years old, and Gauss is only 6 years old. 19th century, the number of scientific research magazines surged. 18 10 founded the world's first pure mathematics magazine. 1826 founded Pure Mathematics and Applied Mathematics by crell (1780- 1855). 1835, the Paris Academy of Sciences also founded the weekly magazine, which summarized the latest achievements in four pages. It is said that this is to limit Cauchy because he always writes a lot. 1878 America founded its own mathematical magazine.
/kloc-in the 0/9th century, mathematicians' societies appeared to promote mathematical research, such as London Mathematical Society (1865), French Mathematical Society (1872), American Mathematical Society (1888) and German Mathematical Society (1890). They get together regularly to read newspapers, and each club sponsors some.
/kloc-in the 0/9th century, mathematics developed greatly. With the spread of knowledge, more scholars appeared, and the small mathematician aristocratic group was replaced by the big collective. In the18th century, there were signs that Euler was the son of a shepherd, D'Alembert was the illegitimate child of the poor family, gaspard monge was the son of a small trader, and Laplace was born in a peasant family. I feel that the purpose of double reduction is the same as Project Hope and compulsory education. The country does not want to be a problem solver, but hopes to reduce the competitiveness of cities and give students in areas with poor educational resources more opportunities to get ahead. ) Universities participated in research, textbooks were published, and the system of systematically training scientists initiated by Napoleon created many mathematicians.