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The 19th century was an auspicious scene in mathematics. ∶ Lagrange was still active in the field of mathematics. Laplace was at the peak of his intelligence. Fourier devoted himself to studying his 1807 manuscript, which was later incorporated into his classic Hot Theory (1822). Gauss just published his study of arithmetic (1801), which was a milestone in number theory, and then he made many contributions, winning him the title of prince of mathematics. Cauchy, Gauss's French counterpart, showed extraordinary talent in an 1814 paper.

Through a brief introduction to the work of these people, we can see that great progress was made in discovering the mysteries of nature in the first half of the 19th century. Although Gauss made great contributions in mathematics, he devoted most of his time to the study of physics. In fact, he has been a professor of astronomy and director of the Gottingen Observatory for nearly 50 years. Astronomy takes up most of his time and energy. He made his first remarkable achievement in 1801, when Piage discovered the asteroid Ceres on January 1 that year. Although it could only be observed for a few weeks, Gauss, then only 24, used a new mathematical method in his observation. And predicted the trajectory of the planet. The observation at the end of the year is very close to Gauss's prediction. When Obers discovered another asteroid, Jupiter, in 1802, Gauss once again succeeded in calculating its trajectory. In one of Gauss's main works, the Theory of Celestial Motion, all these early works in astronomy are summarized.

Later, at the invitation of the Duke of Hanover, Gauss made a survey of Hanover, established geodesy, and produced the creative idea of differential geometry. He also achieved great success in the physical study of theoretical and experimental magnetism between 1830 and 1840, when he created a method for measuring the earth's magnetic field. Maxwell, the founder of the theory of electromagnetic fields, said in his Theory of electricity and magnetism that Gauss's magnetic research reconstructed the tools used by the entire scientific ∶, the methods of observation, and the calculation of results. Gauss's paper on geomagnetism is a model of physical research. To commemorate this work, the unit of the magnetic field is called Gauss.

Although Gauss and Weber did not invent the idea of the Telegraph, in 1833 they designed a practical device that deflected the pointer to the left or right, depending on the direction of the current on the wire. This is just one of several inventions of Gauss. He also works in optics, a subject that has been neglected since Euler's time. His research from 1838 to 1841 laid a new foundation for dealing with optical problems.

In the 19th century, Cauchy can compete with Gauss in the field of mathematics. Cauchy has more than 700 mathematical papers with a wide range of interests, second only to Euler in number, involving all branches of mathematics. He is the founder of the function theory of complex variables. But Cauchy devotes at least as much energy to physics as to mathematics. In 1815 he was awarded an award by the French Academy of Sciences for a paper on water waves. He wrote groundbreaking works on the balance of rods and elastic films (such as metal sheets) and waves in elastic media. He is also the founder of the branch of mathematical physics. He worked on the theory of light waves created by Fresnel and extended it to the field of light decomposition and polarization. Cauchy is a first-rate mathematical physicist.

Although Fourier's work is not exactly in the same field as Gauss and Cauchy, his work is particularly worth mentioning because he has brought more substantial progress to the conduction of heat in mathematics. Fourier regards this subject as the most important one in the study of the universe. Ring, because the study of the heat conduction in the interior of the earth may prove that the earth is formed by cooling and solidification from a molten state, so that some estimates of the age of the earth can be made. In the course of this work, he developed the theory of infinite trigonometric series, now called Fourier series, so that it can be used in many other fields of applied mathematics. It is not too much to praise his work in any word.

The achievements of Gauss, Cauchy, Fourier and hundreds of others seem to be irrefutable evidence that more and more ∶ truths about nature are being revealed. The fact is that throughout the 19th century, mathematical giants have been moving forward along the path laid by their ancestors, creating a more powerful mathematical method and successfully applying it to the further exploration of nature. They accelerate their search for the mathematical laws of nature, and they seem to be driven by such a belief that ∶ they were sent by God to reveal God's intentions.

If they pay a little attention to the behavior of some of their peers, then perhaps they will be prepared for the coming disaster. Bacon has long written about ∶ in his New tools (1620).

The concept of a group is innate and closely related to the group and race. As a result, human feelings are sometimes mistakenly regarded as the standard of things. On the other hand, all sensory or mental perception depends on man, not on the universe. And the human mind is like an uneven mirror, assigning its own nature to things. Light comes from things, but mirrors distort them.

In the same book, Bacon advocated using experience and experiments as the basis of all knowledge, he wrote

The axioms established by reasoning are not enough to produce new discoveries, for the mysteries of nature are far better than the mysteries of reasoning.

Even the most faithful believers will unwittingly disagree on what leads to the weakening of God's role in designing the universe.

Both Copernicus and Kepler regard their heliocentric theory as proof of God's mathematical wisdom. But it conflicts with the importance of man in the Bible. Galileo, Boyle and Newton insist that the purpose of their scientific research is to prove the intention and existence of God, but in fact they seldom involve God in their work. Of course, as we can see, Galileo believed in God's mathematical design, and he said this only to show that other mysterious or supernatural forces should not be introduced in explaining the mysteries of nature.

In Galileo's time, the belief that Almighty God could change his design dominated. Descartes, on the other hand, declared that the laws of nature were unchangeable. This undoubtedly limits the power of God. Newton also believed in the inherent order of the universe and expected God to keep the world running according to his own will. He compared it to the watchmaker repairing the clock to make it work properly. Newton had every reason to believe that God created ∶, although he knew very well that the trajectory of a planet was not a true ellipse because the trajectory of another planet was influenced by other planets, but he could not mathematically prove that this deviation was due to the gravity of other planets, so he believed that it was impossible to maintain the stability of the universe unless God continued to make the universe work according to his own plan.

Leibniz opposes this view, and in his letter to the philosopher Clark, Newton's advocate and philosopher, in November 1715, he commented on Newton's ∶ of God's view that God often needs to repair and wind the universe.

God doesn't seem to have enough foresight to keep the world moving forever. In my opinion, the force and energy in the world are constant, transferring from one part of matter to another according to the laws of nature.

Leibniz accused Newton of denying God's power. In fact, Leibniz accused Newton of weakening Britain's faith.

Leibniz was right. Newton's work inadvertently separated or liberated natural science from theology for the first time. Galileo insisted that natural science must be separated from theology, and Newton took a big step towards a purely mathematical explanation of natural phenomena by adhering to this principle in his book principles. So God is more and more excluded from the mathematical description of scientific theory. In fact, the anomalies that Newton could not explain were fundamentally explained in later studies.

The universal law that restricts the movement of celestial bodies and ground objects gradually dominates the whole intellectual community, and the consistency of predictions and observations shows the perfection of this law. Although after Newton, some people still think that this perfect design was made by God, God has retreated behind the scenes. The mathematical laws of the universe became the focus. Leibniz noticed that Newton's "principles" implied that ∶, with or without God, the world still has its own way. The pursuit of pure mathematical results has gradually replaced the focus on God's design. Although many mathematicians after Euler still believe in the existence of God, believe in God's design of the world, and that the main function of mathematics as a science is to provide tools to decipher this design, however, with the further development of mathematics and more subsequent development, mathematical research has received less and less revelation from God, and the existence of God has become blurred.

Although born in a Catholic family, Lagrange and Laplace are atheists. Laplace completely denied that God was the mathematical designer of the world. There is a famous story that when Laplace presented his "astromechanics" to Napoleon, the latter said ∶, "Mr. Laplace, they told me that you wrote this book about the cosmic system without mentioning its creator at all." Laplace is said to have replied to ∶, "I don't need this hypothesis." Nature replaced God, and as Gauss said, ∶, "you, nature, my goddess, my contribution to your laws is limited." Gauss is convinced that there is a God who is omnipresent, omniscient and omnipotent, but he believes that God has nothing to do with mathematics and the exploration of the mathematical laws of the universe.

Hamilton's work on the principle of least action also revealed a shift in intellectual views. In an article in 1833, he wrote that ∶

Although the minimum action theorem has been based on the highest theorem of physics, from the base of cosmic economy, people generally refused to regard it as the law of the universe at that time. In this regard, rejection is precisely for other reasons, in fact, camouflage savings are often wasted. Therefore, we cannot assume that this amount of saving is designed by the mind of the God of the universe. However, a certain degree of simplicity can be considered to be included in this idea.

In retrospect, the creed that nature is God's mathematical design is being undermined by the work of mathematicians. Scholars increasingly believe that human reasoning is the most powerful tool and the best proof, because it is the result of mathematicians. Not all 19th century mathematicians denied the status of God. Cauchy accused people of "not hesitating to abandon all hypotheses that contradict the theorems that have been discovered." However, the belief that God is the mathematical designer of the universe is beginning to decline. The decline of this belief soon gave rise to the question of why the mathematical laws of nature must be true. One of the first people to question the truth was Diderot. In his "Natural explanation", mathematicians like gamblers ∶ both gamble with abstract rules invented by themselves. The subject of their research is just a rule with no basis for facts. The scholar Feng Dengli is also critical of this in his book the pluralism of the World (1686). His attack on the immutability of the laws of motion of celestial bodies is that the gardener will never die as long as the roses are in bloom.

This article comes from the official account of Wechat: Lao Hu Shuo Science (ID:LaohuSci). Author: I am Lao Hu.

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