Author | Sun Qingxian
Source | Journal of Science Grand View Garden
Famous mathematicians all have a high degree of mathematical history, and their achievements have largely drawn rich nutrients from the sages of their predecessors.
Mathematics has a very high historical and cumulative, compared with physics, physiology and other disciplines of knowledge, there is only an expansion, there is no major correction, for example, the Greek philosopher Aristotle put forward the "geocentric theory" view in Ptolemy's famous book "Astronomical Masterpiece" promoted, once became the best astronomical system, which existed in the field of Western astronomy for more than 1,000 years, but with the continuous improvement of astronomical observation technology and the development of navigation and many other social factors to promote, Copernicus questioned Ptolemaic's theory, and in 1539 he wrote the eons-old work The Theory of celestial motion, which systematically discussed the theory of "heliocentrism". Later, Newton discovered gravity, thus completely overturning Ptolemy's "geocentric theory" because it was wrong.
In the field of physiology, Aristotle believed that the blood vessels of the human body were filled with "yuan qi", and did not give how yuan qi worked. Until 199, the ancient Roman physician Galen affirmed that the human blood vessels were filled with blood rather than "yuan qi", but he regarded blood as something produced from the liver, and when the blood flowed through the body, the nutrients were absorbed by various parts of the body and slowly consumed. Then in 1628, the English doctor Harvey published the famous book "On the Movement of Heart And Blood", in which Harvey believed that the blood of the human body is circulating, it flows out of the heart, through the arterial blood vessels, into the venous blood vessels, and then back to the heart, the blood in the blood vessels continue to circulate. Engels spoke highly of Harvey's contribution: the discovery of blood circulation established physiology as a science. However, the conclusions had not yet been verified, and it was not until 1671 that Galileo Galileo invented the telescope, the Italian anatomist Malbiqui changed the telescope to a microscope to figure out the full path of blood circulation, Harvey's theory of blood circulation was scientifically determined, and so on. In the process of development, other categories of knowledge exist more or less while revising and developing.
Mathematics is developed by mathematicians in the process of continuous inheritance and expansion, its concepts and ideas do not have to be uprooted and overturned, it is slowly grown in a highly inclusive environment. The "Thales theorem" 2600 years ago is valid to this day, just as functional, just as flawless; for example, in the development and perfection of the number system, Hippasias was thrown into the sea because of the discovery of irrational numbers. In the 2500 years of human social development, the logical basis for the existence of irrational numbers did not make any progress until Euler wrote e as an infinite series multiplication of convergent series, proving that e is an irrational number; Lambert used the tangent function to expand into a form similar to a continuous fraction to prove that pi is irrational numbers, and then after Dekind and Cantor established the theory of real numbers, the logical structure of irrational numbers was truly solved.
Every achievement in the development of mathematics requires the efforts of mathematicians for decades, hundreds or even thousands of years to take meaningful steps, and when they grope forward in the fog, there are confusions, abandonments, struggles, and even more scattered in the vast sky after defeat, but the fragmentary results achieved by the adherents will eventually make them become the brilliant stars in the sky of mathematical history, shining brightly. If children can feel their spirit of frustration and undefeated in the mental journey of reading mathematicians, they will also gain the courage to fight tenaciously and overcome difficulties from them.
The establishment of calculus theory condensed the efforts of many mathematicians. At first, in practical applications, Galileo designed the telescope to determine the tangent problem of any point on the surface of the lens; to determine the area swept by the planetary movement, it was necessary to calculate the length of the curve, the area of the curved edge pattern, and so on. There are many scientists who have solved these problems, Kepler's 1615 "New Stereo Geometry of Measuring Barrels" revealed the idea of infinitesimal methods and infinitesimal summation; Descartes used algebraic methods to discuss the structure of normals at the time of light refraction in Geometry published in 1637, which promoted the early development of calculus; in 1635 Cavalieri proposed the principle of non-component in his book "The Geometry of Continuous Non-component Promoted by New Methods", using the infinitesimal method to calculate area and volume Later, when Wallis studied Torricelli's Geometric Operations, he came up with the formula for the integral power of fractions and the arithmetic of infinitesimal analysis. On the road to calculus theory, from Aristotle onwards, there were germs of ideas, but it was not until the first half of the 17th century that the trickle of the sages of the ancestors finally converged on the magical door of calculus. In the end, one of the culminationists was Newton, who left Cambridge University in 1667 to work quietly in the countryside due to the epidemic, and the other was Leibniz. Newton's starting point was mechanics, which was to establish calculus based on the model of speed; Leibniz used the analytical method to establish calculus from the geometric problem.
Calculus is a peak of human intelligence and a great crystallization of human wisdom. Engels once said: "Of all theoretical achievements, there is not necessarily any such thing as the development of calculus in the second half of the 17th century as the supreme victory of the human spirit." "The invention of calculus promoted the Industrial Revolution and laid the foundation for industrial social civilization. With it, mathematics can describe changes and describe movements, and Zhu Rong can reach Mars on schedule. It plays a very important role in the study of the laws of nature and society, and has an extremely far-reaching impact on philosophy and human culture, and is an intellectual struggle that shocks the soul.
If primary and secondary school students can know the good intentions of mathematicians and feel their thoughts, their attitude to science, their spirit of pursuing beauty and truth, I believe that they will feel empathy, and harvest the joy of reading and learning mathematics, and can better perceive the truth of mathematics and make it incomparably beautiful.
Childhood children, in mathematics is a blank piece of paper, when they first contact mathematics, they will feel that the mathematics they learn, as if it is popped out of nowhere, their hearts are full of all kinds of doubts, learning to learn may forget these doubts, learning mathematics has become rote memorization, lost curiosity about mathematics.
For example, some birds can distinguish the collection containing 4 components, the sense of number is not owned by humans alone, but in the long course of history, only humans can recognize that there is something common in the objective facts of a stone and a pile of stones, a sheep and a flock of sheep, a tree and a forest, it is unique, after a one-to-one correspondence, abstracting the only commonality in these objective facts is the number, whether it is a stone, a sheep, or a tree, we all use the symbol 1, 1 is called "number". For example, why does the emergence of irrational numbers cause a crisis in the development of mathematics, and whether imaginary numbers are virtual or not?
The feud between Newton and Leibniz over the invention of calculus, Euler's perseverance while holding the child, his love for Ink, and so on. These questions, the intertwined past of people and things can make children realize the beauty of mathematics, the truth of mathematics, and the interest of mathematics, thus generating the motivation to learn mathematics. Early understanding of the history of mathematical thought is a very important and meaningful step in learning this science.
Chen Shengshen, the great Chinese differential geometrist in modern times, once said: "The purpose of a mathematician is to understand mathematics. Historical advances in mathematics have been done in two ways — by increasing the understanding and generalization of known materials. Poincaré once said: "If we want to foresee the future of mathematics, the appropriate way is to study the history and present situation of the discipline." "It can be seen that the understanding of the history of mathematics and the gradual clarity is an indispensable part of the strong foundation, and the earlier such an understanding, the better.
The purpose of education is not only to let everyone learn more knowledge, but to understand more about the ins and outs of knowledge, so that it can be transformed into their own coping methods and handling skills when they encounter problems. Mathematical knowledge is clearly printed in books, and as long as we can read, it is not difficult to memorize many pages a day. However , when we know that in three-dimensional Riemannian geometry , if the curvature is equal to zero , it is Euclidean geometry ; if the constant curvature is positive , it is Riemann geometry; if curvature is negative , it is Lobachevsky geometry. In Euclidean geometry, the sum of the inner angles of a triangle is 180°, and in the other two geometries, the sum of the inner angles of a triangle is not 180°. Under this systematic understanding, one's understanding of geometry is transparent and has a sudden sense of enlightenment.
In the process of traveling from "ignorance on this shore" to "epiphany on the other shore", sometimes only the curve can be taken, although the curve is very long, but the process of walking through the curve is interesting and useful. This curve is hidden in the meandering Nile, the rich Mesopotamia, the history and culture of the valleys along the Yangtze and Yellow Rivers; hidden in the back of the people who measure temples and altars and pull the rope, hidden in the struggles and defeats of mathematicians, it is priceless. And we sometimes always feel that this is too inefficient, wasting the child's time, it is better to let the child do more problems. But after doing so many problems, children find that they don't know why they have to do so many problems, and our starting point is not just to do one more problem.
Read Euler, he is the teacher of all.
Author: Sun Qingxian (Electronic Industry Press Co., Ltd.), editing and publishing direction for mathematical culture, mathematical reading, a brief history of mathematics, natural science and other popular science books, committed to protecting and stimulating children's curiosity of science popularization work, has planned to edit and publish "Where is Mathematics Revised Edition", "Wonderful Mathematics Here" and "My Favorite Fun Math Book" and so on.
◎ Special reviewer Li Wenlin
◎ Art Editor Zhang Tingting
◎Article source Science Grand View Garden Magazine