Strict logical argumentation and deductive reasoning are the core of rational thinking, so mathematical thinking ability plays a unique and irreplaceable role in the formation of rational thinking. Einstein once commented on Euclid geometry: "The world witnessed the miracle of a logical system for the first time. This logical system moves forward step by step accurately, and every proposition of it is absolutely unquestionable ―― I am talking about Euclidean geometry here. This admirable reasoning victory has given the confidence necessary for the future achievements of human reason. "
In his biography, Mr. Shen Junshan, the former headmaster of Tsinghua University, Taiwan Province Province, recalled with emotion his study of plane geometry in junior high school: at that time, after class, every child had to arrange some housework, and one of the tasks assigned to me was "herding sheep". In order to give milk to my newborn cousin, I have a sheep at home, and I have to take it to the nearby grass every afternoon to let it eat fresh grass. This is my favorite time of the day. In a hurry to finish other housework, I took the sheep out and tied it under the big elm tree with a long rope, so that it could find grass round and round. I broke branches from the tree as compasses and rulers, and solved one geometry problem after another under the tree. When I first arrived in Shaanxi, I was not used to my new home and school. I was a lonely child. Only under the elm tree, immersed in rational pleasure alone, is my most complacent time. After the second day of junior high school, there was no geometry class and no sheep, so I made some new friends at school. However, going to Yushu to think about new geometric propositions is still my most cherished time alone, and I sneak away to do it whenever I have the chance. By the time I graduated from junior high school and left Wushu (Shaanxi place name), I had accumulated four exercise books and kept them for a long time. Of course, they are of little value. The Greeks solved it two thousand years ago, but the training that brought me thinking and reasoning made me endless. If you want to ask which course will benefit you the most in this life, it is undoubtedly geometry. It seems to wash away your thoughts and make them clear.
Examples of rigorous mathematical calculation and deductive reasoning are everywhere in reality. 1846, Le Ye Wei discovered Neptune on the tip of a pen through calculation, which is a legendary story in the history of science.
1781March 3, the famous British astronomer William? After Herschel discovered Uranus, when some astronomers in the world calculated the orbit of Uranus according to Newton's gravity theory, they found that the calculated results were always inconsistent with the actual observation position. This can't help but make people think: is there something wrong with Newton's theory, or is there another celestial gravity acting on Uranus? 1845, Adams, a 26-year-old young teacher at Cambridge University in England, thought that there was a big planet outside Uranus' orbit through calculation and research. It is the gravity of this unknown planet that makes the theoretical calculation inconsistent with the actual observation position. He also calculated and predicted the position of this unknown big planet in the sky. However, his prediction did not attract the attention of the astronomers concerned. Similarly, in the summer of 1845, French astronomer Le Ye Wei independently predicted the position of this unknown planet outside the orbit of Uranus in the sky through calculation. According to Le Ye Wei's predicted position, Gale, the head of astronomy in Berlin, Germany, discovered this giant planet on September 23rd, 1846. It was found only 52 degrees away from the position predicted by Le Ye Wei and 2 degrees and 27 minutes away from the position predicted by Adams. The discovery of Neptune expanded the boundary of the solar system by about 65.438+0.7 billion kilometers. The discovery of Neptune is a brilliant achievement of celestial mechanics laid by Newton and a model of theory guiding practice.
1990, Iraq ignited hundreds of oil wells in Kuwait, and smoke covered the sky. The United States and its allies have seriously considered the consequences of all oil wells being ignited before carrying out military operations in desert storm. According to the American Supercomputing Review, the Pentagon asked Pacific Serra Research to study this issue. Naville-Stokes equation and energy equation with heat loss are used as calculation models. After a series of simulation calculations, it is concluded that the smoke from the fire may cause major pollution events, affecting the Persian Gulf, southern Iran, Pakistan and northern India, but it will not get out of control, causing global climate change and irreparable damage to the earth's ecology and economic system. Only in this way can the United States make up its mind to take military action. So people say that World War I is a chemical war (gunpowder), World War II is a physical war (atomic bomb), and the Gulf War is a mathematical war.
Bacon once said that mathematics is "the key to science". Galileo said, "The great works of nature are written in the language of mathematics." The laws of physics, as well as many basic scientific principles, are expressed in mathematical language. The idea of gravity has a long history, but it became the most important and famous law of gravity in science only after Newton expressed it with precise mathematical formula. Einstein thought: "Theoretical physicists have to obey the domination of pure mathematical forms more and more." He also believes that "the principle of creativity lies in mathematics" in theoretical physics. His own work confirmed this idea, and it was Riemannian geometry that provided a mathematical framework for general relativity. The work and thoughts of the masters of science led to the following belief: "We live in a universe limited by precise mathematical laws." It is this restriction that makes the world recognizable. The knowability of the world is the most important principle in materialist epistemology. People introduce calculation into the scientific community as a third scientific method independent of theory and experiment.
Today's research on mathematics education shows that mathematics is not only a science in digital world, metaphysical world or wider world, but also a science full of humanistic spirit. We should give full play to the humanistic education function of mathematics, and cultivate students' culture and personality with the ideological system of mathematical science, the aesthetic value of mathematics and the innovative spirit of mathematicians, so as to cultivate students' emotional attitude and values.
Some people may worry, in actual teaching activities, if we dig deep into the humanistic education function of mathematical thought and educate students on their emotional attitudes and values, will it affect normal classroom teaching? In fact, this kind of education is not too much, but too little, because this kind of deep excavation requires typical mathematical thinking methods, and it also requires us to constantly learn, discover and accumulate in teaching and life.