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How big is the mathematician's brain in discovering the devil who can predict the universe? "

He is a rare generalist in the history of science, the founder of probability theory, an important pioneer of modern astronomy, and is known as the pioneer in the field of applied mathematics. He is Biel Laplace known as "Newton in France".

Born in Beaumont, Normandy, France, on March 23, 1749, Biel Laplace showed extraordinary mathematical talent from an early age. During their study in university, the two teachers who taught mathematics were very famous. One was Christopher Gadbrad and the other was Pierre Likanu. These two teachers devoted their love of mathematics to mathematics education. It was they who ignited Laplace's enthusiasm for mathematics and fully developed Laplace's mathematical talent. They agreed that Laplace should continue to develop in mathematics.

At the age of 18, Laplace came to Paris with a letter of recommendation from Likanu in order to realize his mathematical ideal. At this time, D'Alembert was already a leading figure in French mathematics, and his first request was refused. Laplace was not reconciled and sent a paper on mechanics, which showed Laplace's talent and finally knocked on D'Alembert 's door.

But as Laplace's grandfather recalled, D'Alembert was not interested in the young man, and in order to scare him away, he threw him a thick, heavy math book and said coldly, "wait till you finish reading this book." A few days later, Laplace came again. D'Alembert was still unfriendly and wondered if he had really finished reading it, even if he had flipped it. A few random questions were asked, and D'Alembert gave a quick and accurate answer, and D'Alembert knew that the young man was not lying. He asked Laplace a few more difficult questions, and it took Laplace all night to solve them. D'Alembert was surprised to find that he was a rare talent. since then, Laplace has not only become D'Alembert 's assistant and proud disciple, but also has a stable teaching job and solved his livelihood worries. to be able to devote himself to mathematical research.

On March 28, 1770, Laplace submitted his first paper to the French Academy of Sciences, which cleverly proved the maximum and minimum curvature of Lagrange. Although it was only read at the meeting and was not published, Laplace's mathematical talent began to attract the attention of the French mathematical community, when he was only 22 years old.

On July 18, 1770, he published another paper on differential equations, while translating the first paper into Latin and published in a mathematical journal in Leipzig in 1771 (four years later, he revised the paper and republished it in 1774).

In 1771, he again sent a paper on the integration of differential equations, which has important applications in mechanics and astrophysics.

Because of his achievements in the past two years, he was nominated as a member of the French Academy of Sciences, but Vandermont, a mathematician and musician known for his determinant theory, was given priority in the election. Laplace ran again the following year, but this time the philosopher Victor Coulson was elected. Laplace, 23, is full of blood, and he thinks the academic level of the first two is not as good as him. D'Alembert was also disappointed. In 1773, New Year's Day wrote a letter to Lagrange, director of the mathematics department of the Berlin Academy of Sciences, asking if Laplace could run for membership of the Berlin Academy of Sciences. Just before Lagrange replied, on March 31, 1773, Laplace was elected a member of the French Academy of Sciences. In this campaign, he read out 13 papers published in the previous three years. The Secretariat of the Academy of Sciences said in the filing that Laplace created a new historical record for the French Academy of Sciences to recruit members with a large number of and high-quality papers.

Laplace's contribution to applied mathematics and probability theory reached the highest level in the field of mathematics at that time. His Theory of probability was published in 1812, in which universal functions were studied, differential equations, difference equations, probability and statistics were established and developed. In the theory of probability, he first gave the definition of some important concepts, clarified the confusion of the previous probability theory, discussed the approximate theory of variables, and developed Bayesian statistical interpretation (called Poincare theorem many years later). He built the Laplace equation and created the Laplace principle, and his achievements have been applied in many branches of theoretical physics. In the study of probability theory, Laplace's "determinism" philosophy has a great influence on later generations. His "Laplace demon" (Laplace demon: this "demon" knows the exact position and momentum of each atom in the universe. Newton's laws can be used to show the whole process of cosmic events, the past and the future. He became famous for a while, which made him a representative figure of "determinism" thought.

In astromechanics, many of Laplace's achievements are groundbreaking. On November 27, 1771, as a mathematician, he first dabbled in astrophysics and published a paper on the study of planetary motion using mathematics. Since then, his research has focused on probability theory and celestial mechanics, and many of his achievements still have high reference value.

From 1773 to 1776, according to Newton's theory of gravity, Laplace calculated the motion of celestial bodies by using differential equations, solved the precession of planets under the interference of multi-body motion, discussed the orbits of Saturn and Jupiter, which plagued astronomers at that time, and the circular motion of the moon; studied the shape and tidal motion of stars; proved the stability of the solar system. From 1776 to 1813, together with Louis Lagrange, he established a strict and precise new standard for azimuth astronomy; his new planetary watch was widely used in 19th century astronomy.

In the solar system, why do the eight planets maintain long-term stability under mutual interference? this puzzling problem involves complex and difficult calculations of multi-body motion, which has not been solved for a long time. In 1786, Laplace completed the calculation of multi-body motion and obtained the planetary precession caused by the interaction of multi-body motion, but he mathematically proved that the order of magnitude of these precession is not only very small compared with its orbital motion. and it can be "self-repairing", so the whole solar system is stable. He further discussed the shape of the earth and the tidal motion of the oceans. He combined these results and published them in the principles of Celestial Mechanics, published in 1789. This masterpiece made astronomy leap from "observation" to theoretical research, which demonstrated Laplace's mathematical talent. Through his hands, mathematics not only created theoretical astronomy, but also made astronomy a breakthrough in the development of applied mathematics.

In 1796, Laplace published another monograph on the origin of the solar system. In this book, after reviewing the historical development of astronomy, he put forward the hypothesis of the origin of nebulae in the solar system, which is a very constructive thinking. Through probability calculation, his view of comets is very close to that of modern cataclysm. "although the probability of comets colliding with the Earth for thousands of years is very small, it is not difficult to imagine that such an impact has had serious consequences for the Earth," he said. for example, the earth's axis has shifted, the oceans have left their original position, and humans and animals have been buried in large global floods or burned in strong global tremors. " What is more commendable is that he was the first to predict the existence of "black holes" and "gravitational collapse".

At the end of the principles of Celestial Mechanics, he made a very instructive remark, he said: "if a person is limited to collecting phenomena, such a scientist is only a 'flower in a greenhouse'. It is impossible for him to recognize the great laws of nature. Only by comparing various phenomena with each other and digging out the deep-seated relationship can we find out the rules." Laplace's "deep" mining has the application of mathematical theory, which is also a summary of his scientific thoughts and research methods.

The statue in Beaumont, Laplace's birthplace, became a member of the French Academy of Sciences in 1785. Under his leadership, the French Academy of Sciences developed standards for measuring weight, and the committee included Lavissier, Baoda, Columbus, Brisson and D'Alembert.

In the 1880s, Laplace's great achievements made him not only well-known in the field of mathematics, but also influential in other fields, in which he far surpassed his mathematical counterparts. He used quantitative methods to study all kinds of realistic systems, both physical and astronomical, and he even worked with Lavissier to extend his mathematics to the field of chemistry, where he studied chemical heat phenomena. became the beginning of physical chemistry.

After 1780, Laplace's work in physics has gone far beyond the scope of mechanics. Because of the depth of the problems involved and the high level of theory, it has had a great impact on the later stage. For example, he believes that as long as the distance and the form of interaction between molecules in a gas are determined first, many related phenomena can be analyzed. He tried to use this method to determine the relationship between gas pressure and density in the container, atmospheric pressure, atmospheric refraction, capillarity, the velocity of sound propagation and some thermal theories.

After 1806, from the point of view of elastic fluid, he discussed the shape change caused by spin in the process of the earth from heat to cooling, and later even discussed the propagation of gravity from a philosophical point of view. These studies continued until 1821, when he was 72 years old. These results were later edited into his Analytical Theory published in 1820.

The first edition of Laplace's series published by the Academy of Sciences in Paris, France, Laplace was born into a Catholic family, but he himself is an atheist. He denied that "God is the mathematical designer of the world". There is a famous story that when Laplace presented his "astromechanics" to Napoleon, Napoleon said to him, "Mr. Laplace, they told me that you wrote this book about the cosmic system, but did not mention its founder at all." Laplace is said to have answered simply: "I don't need that assumption." For Laplace, the world is as certain as a clock.

Under the leadership of Laplace, the French mathematical community not only flourished for a while, but also became an active participant in physics and chemistry, resulting in a small group of frequent contacts. Among them are D'Alembert, Lagrange, Legendre, Biot, Poisson, Arago and others. Their work not only strongly influenced the research direction of physics and chemistry, but also created and developed a precedent in the research of applied mathematics, making it an independent field in mathematics. Laplace became a leader in this research and was called "the forerunner of applied mathematics".

Source: 365 days in the History of Science, slightly edited by: Wei Fengwen Wu Yi Editor: Zhang Runxin this article comes from the official account of Wechat: Origin Reading (ID:tupydread), author: Wei Fengwen, Wu Yi, Editor: Zhang Runxin

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