He described gravity and three laws of motion in the paper "Laws of Nature" published by 1687. These descriptions laid the scientific view of the physical world in the next three centuries and became the basis of modern engineering. By demonstrating the consistency between Kepler's law of planetary motion and his theory of gravity, he showed that the movements of ground objects and celestial bodies all follow the same natural law; It provides strong theoretical support for the sun-centered theory and promotes the scientific revolution.
In mechanics, Newton expounded the conservation principle of momentum and angular momentum and put forward Newton's law of motion [1]. In optics, he invented reflecting telescope, and based on the observation that a prism diverges white light into the visible spectrum, he developed the color theory. He also systematically expressed the cooling law and studied the speed of sound.
In mathematics, Newton and Gottfried Wilhelm Leibniz shared the honor of developing calculus. He also proved the generalized binomial theorem and put forward Newton's method to approximate the zero point of function, which contributed to the study of power series.
In economics, Newton put forward the gold standard.
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.
One of Euler's Contributions —— Fluid Mechanics
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. However, because the basic equation was first proposed 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 formula
It shows the relationship between trigonometric function and imaginary number, can be used to find the logarithm of complex number, and 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.
One of Euler's Contributions —— Topology
Last but not least, Euler made an important contribution to the use of mathematical symbols. 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.
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 dedication to 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.
Euler on German stamps
Therefore, some people may ask why Michael Hart, an American scholar, did not rank Euler in a higher position in his book The Most Influential People in History. The main reason is that although Euler has made outstanding achievements in demonstrating how to apply Newton's laws, he has never found any original scientific laws himself, which is also the reason why William Conrad, Roentgen, Mendel and others rank high. Each of them mainly discovered new scientific phenomena or laws. Nevertheless, Euler made great contributions to science, engineering and mathematics. [ 1][ 12][ 13]
Main evaluation
Euler can easily calculate, just like a man breathing and an eagle flying in the air.
French mathematician Laplace
-arago (arago)
Learning Euler's works is the best tool to understand mathematics.
-Johann Carl Friedrich Gauss (Gauss)
Today's students can benefit from Euler's introduction to infinite analysis, which is unmatched by any modern textbook.
-A. Weil (Waier)
Read Euler's works. In any sense, he is our master.
-Pierre-Simon Laplace (Pierre-Simon Laplace)
When I introduced advanced analysis, it was a child, and you brought it up.
—— johann bernoulli (johann bernoulli)