1750, Euler listed some properties of polyhedron in a letter to Goldbach. One of them is that if V, E and F are used to represent the number of vertices, edges and faces of a closed convex polyhedron, then V-E+F = 2. The following year, he gave a proof of this property. Although Descartes was discovered long after 100. The first person to understand the meaning of V-E+F seems to be Euler. He is interested in this relationship because he wants to use it to classify polyhedrons. The Euler characteristic line V-E+F proposed by H Poicaré and its generalization in multidimensional complex is one of the main invariants of modern topology. Chen Shengshen said simply.

(Excerpted from the Biographical Dictionary of Mathematicians in Zhang Hongguang)

Euler was the best mathematician in18th century and one of the greatest mathematicians in history. /kloc-In the 8th century, Swiss mathematician and physicist Lennart Euler has been one of the most outstanding scientists in the world. All his creations are widely used in the whole physics and many engineering fields. Euler's achievements in mathematics and science are unbelievable. He wrote thirty-two long books, several of which were more than one volume, and also wrote many creative mathematical and scientific papers. His scientific works amount to more than seventy volumes. Euler's genius has enriched every field of pure mathematics and applied mathematics, and his achievements in mathematical physics have infinitely broad application fields. ?

As early as last century, isaac newton put forward the basic laws of mechanics. Euler was particularly good at demonstrating how to apply these laws to some common physical phenomena. For example, he applied Newton's law to fluid motion and established fluid mechanics equations. Similarly, by carefully analyzing the possible motion of a rigid body and applying Newton's law, he established a set of equations that can completely determine the motion of a rigid body. Of course, in practice, nothing is completely rigid. Euler also contributed to elasticity, which is a theory to study how solids deform under external forces. ?

Euler's genius also lies in his mathematical analysis of astronomical problems, especially how the three bodies, the sun, the moon and the earth, move under the interaction of gravity. This problem-a problem that still faces in 21century-has not been completely solved. By the way, Euler was a unique and outstanding scientist in the18th century. He supported the light wave theory, and it turned out that he was right. ?

Euler's rich mind often opens the way for others to make famous discoveries. For example, the French mathematician and physicist Joseph-Louis Lagrange created a set of equations called "Lagrange Equation". This equation is very important in theory and can be used to solve many mechanical problems. But because the basic equation was first put forward by Euler, it is usually called Euler-Lagrange equation. It is generally believed that another French mathematician, jean baptiste joseph fourier, created an important mathematical method called Fourier analysis, and its basic equation was originally founded by lennert Euler, so it is called Euler-Fourier equation. These equations are widely used in many different physical fields, including acoustics and electromagnetism. ?

In mathematics, he is particularly interested in two fields of calculus-differential equations and infinite series. He has made very important contributions in both aspects, but the description here is too professional. His contributions to variational calculus and complex mathematics laid the foundation for all the achievements made later. These two subjects are not only of great significance to pure mathematics, but also widely used in scientific work. Euler's formula eiQ = cosθten isθ represents the relationship between trigonometric function and imaginary number, which can be used to find the logarithm of negative numbers. It is one of the most widely used formulas in all mathematical fields. Euler also wrote a textbook of analytic geometry, which made great contributions to differential geometry and general geometry. ?

Euler is not only handy in making mathematical inventions that can be applied to science, but also has almost the same outstanding talent in the field of pure mathematics. But many of his contributions to number theory are too profound to be described here. Euler was also a pioneer in the field of topology, a branch of mathematics, which became very important in the twentieth century. ?

Last but not least, Euler made an important contribution to the making of mathematical symbols used now. For example, he proposed the Greek letter π commonly used in pi. He also introduced many other simple symbols, which are often used in mathematics now. ?

Euler was born in 1707 in Basel, Switzerland. He was admitted to university of basel at the age of thirteen. I studied theology at first, and soon changed to mathematics. He got his master's degree in university of basel at the age of seventeen, and at the age of twenty, he was invited by Catherine I to join St. Petersburg Academy of Sciences. At the age of 23, he became a professor of physics at the institute. At the age of 26, he succeeded the famous mathematician daniel bernoulli and became the director of the Institute of Mathematics. Two years later, he was blind in one eye, but he continued to work with great enthusiasm and wrote many excellent papers. ?

174 1 year, frederick the great of Prussia lured Euler from Russia to join the Berlin Academy of Sciences. After 25 years in Berlin, he returned to Russia on 1766. Soon, his other eye also lost its light. Even if such a disaster came, he didn't stop his research work. Euler has amazing mental arithmetic ability. He published first-class mathematical papers until his last breath. He died in St. Petersburg on 1783 at the age of 76. Euler was married twice and had thirteen children, but eight of them died in infancy. ?

Even without Euler, all his discoveries will eventually be made by someone. But I think, as a measure of this situation, we should ask such a question: If no one can make his discovery at all, what will be the difference between science and the modern world? As far as lennert Euler is concerned, the answer seems clear: without Euler's formulas, equations and methods, the progress of modern science and technology will lag behind, which actually seems unimaginable. Looking through the index of mathematical physics textbooks, we will find the following photos: Euler angle (rigid body motion), Euler constant (infinite series), Euler equation (fluid mechanics), Euler formula (compound variable), Euler number (infinite series), Euler polygonal curve (differential equation), Euler function theorem (differential equation), Euler transformation (infinite series) and Bernoulli-Euler law. ?

Euler's works are vast, not only containing scientific ideas, but also full of scientific ideas. He left a very rich scientific heritage and spirit for science to future generations. Historians rank Euler, Archimedes, Newton and Gauss as "four outstanding figures" in the history of mathematics. Nowadays, in many branches of mathematics, we can often see important constants, formulas and theorems named after him. ?

(Quoted from 100 People Affecting the World Process)

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