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Complete works of leonhard euler Euler
"Euler's calculation seems effortless, just like a person breathing, like an eagle hovering in the wind." (arago said), this sentence is not an exaggeration for Euler's unparalleled mathematical talent. He is the most prolific mathematician in history. His contemporaries called him "the embodiment of analysis". Euler wrote a long academic paper as easily as a quick-witted writer wrote a letter to a close friend. Even if he was completely blind in the last 17 years of his life, it didn't stop his great fertility. If blindness has any effect, it is to improve his inner thinking imagination.

How many works did Euler create? It was not until 1936 that people knew for sure. However, it is estimated that it will take 60 to 80 volumes to publish Euler's anthology. Petersburg College spent 47 years sorting out his works. From 65438 to 0909, the Swiss Federation of Natural Sciences began to collect and publish the academic papers of Euler's anthology. This work has been funded by many individuals and mathematical groups all over the world. This just shows that Euler belongs to the whole civilized world, not just Switzerland. The budget carefully prepared for this work (1909 coins about 80,000 dollars) was completely broken by the unexpected discovery of a large number of Euler manuscripts in St. Petersburg (Leningrad). Euler's mathematical career began in the year when Newton died. For a genius like Euler, it is impossible to choose a more favorable era. Analytic geometry (published in 1637) has been used for 90 years, calculus for about 50 years, and Newton's law of universal gravitation, the key of physical astronomy, has been used in mathematics for 40 years. In each of these fields, a large number of isolated problems have been solved, and obvious attempts have been made to unify them everywhere. However, the whole mathematics, pure mathematics and applied mathematics have not been systematically studied as later. In particular, the powerful analytical methods of De Kratos, Newton and Leibniz have not been fully utilized as later, especially in mechanics and geometry.

Algebra and trigonometry at that time had been systematized and developed at a lower level. Especially the latter, has been basically improved. Euler also proved that he is indeed a master. In fact, one of the most striking features of Euler's versatility is that he has the same ability in two branches of mathematics-continuous mathematics and discrete mathematics.

As an mathematician, Euler has never been surpassed by anyone. Perhaps no one can approach his level except jacoby. Algorithmists are mathematicians who design algorithms to solve various special problems. For a simple example, we can assume (or prove) that any positive real number has a real square root. But how can we work out this root? There are many known methods, and algorithm scientists should design practical concrete steps. For example, in Diophantine analysis and integral calculus, it is often impossible to solve the problem until one or more variables are skillfully (often simply) transformed by the functions of other variables. Algorithmists are mathematicians, and they will naturally find this trick. They don't have any identical procedures to follow. Algorithmists are like people who can write limericks at will-they are born, not made.

When a truly great algorithm comes out of nowhere like India's Lo Manu, even experienced analysts will hail it as a gift from heaven: his magical insight into seemingly unrelated formulas will reveal hidden clues from one field to another. So that analysts can find new topics for them to find these clues. Algorithmists are formulists, and they like beautiful forms for the formula itself. Before talking about Euler's quiet and interesting life, we must introduce two environmental factors of his time, which promoted his amazing activity and guided his activities.

In Europe in the18th century, universities were not the main centers of academic research. Without the classical tradition and its imaginable hostility to scientific research, universities could have become the main center. Mathematics was rigorous enough for ancient people to be valued; Physics is relatively new and is suspected. In addition, in universities at that time, mathematicians were expected to devote most of their energy to basic teaching. As for academic research, if it is carried out, it will be a useless luxury, just like ordinary universities in the United States today. At that time, researchers in British universities were able to complete their chosen topics well. However, they are seldom willing to choose any topic. Anyway, what they have achieved or what they have not achieved will not affect their jobs. Under such relaxation, or open hostility, there is no good reason to explain why those universities should be ahead in scientific development, but in fact they are not.

The responsibility of taking the lead is borne by the royal college funded by generous or far-sighted rulers. Frederick the great of Prussia and Queen Catherine of Russia generously gave unrepentant support to mathematics. They made it possible for the development of mathematics to be in the most active period in the history of science for a whole century. For Euler, it was Berlin and St. Petersburg that provided the power of mathematical creation. These two centers of creativity should attribute the inspiration to Euler to Leibniz's enterprising ambition. It was Leibniz who drafted the plan. These two colleges provided Euler with the opportunity to become the most prolific mathematician in history. So, in a sense, Euler is a descendant of Leibniz.

The Berlin Academy of Sciences has declined for 40 years due to lack of brains. Encouraged by frederick the great, Euler gave it a powerful impact and revived it. The St. Petersburg Academy of Sciences, which Peter the Great did not have time to establish according to Leibniz's plan before his death, was established by his successor.

Unlike some colleges today, these two colleges do not take the evaluation of well-written excellent works and the granting of academician qualifications as their main responsibilities. They are research institutions that employ academicians to conduct scientific research. The salary and allowance are generous enough to ensure a comfortable life for the whole family. Euler's family was once no less than 18, and he was enough to make them all live a rich life. /kloc-the last attraction of academician's life in the 0/8th century is that as long as his children have any talents, they will certainly get a good chance to display them.

Next, we will see the second factor that has a decisive influence on Euler's fruitful mathematical achievements. Rulers who provide economic support naturally hope that their money can be exchanged for something other than abstract culture. However, it must be emphasized that once the rulers get a proper return on their investment, they will no longer insist on letting the employees spend their remaining time in productive work. Academician Euler and Lagrange are free to do what they like. There is no obvious pressure to force anyone to produce something that the government can use directly. /kloc-the rulers of the 0/8th century were wiser than the directors of many research institutes today, letting science develop according to their own laws, but occasionally mentioning what they need now. They seem to instinctively realize that the so-called pure research, as long as appropriate hints are made from time to time, will make the urgent practical problems they expect become by-products.

There is an important exception to this general statement, which neither proves nor denies this law. Just in Euler's time, the unsolved problems in mathematical research happened to be related to maritime hegemony, which was perhaps the first practical problem at that time. A country that surpasses all its rivals in navigation technology will inevitably control the ocean. The first problem of navigation is to accurately determine the position of the ship in the sea hundreds of nautical miles offshore, so that it can reach the place of naval battle faster than the enemy (unfortunately, that's why). As we all know, Britain controls the ocean. It can do this, to a great extent, because its navigators can apply the pure mathematical research results in celestial mechanics to practice in the18th century. This practical application is directly related to Euler. Newton was the founder of modern navigation, although he never bothered about this problem himself, and never (as far as people know) set foot on the deck of a ship. Determining the position of a ship at sea depends on the observation of celestial bodies (sometimes this includes Jupiter's satellites on special voyages). Newton's law of universal gravitation shows that, if necessary, with enough patience, the position of the traveling star and the moon phase profit and loss can be calculated in advance within a hundred years. Those who wish to control the ocean will arrange the calculator of the nautical almanac to work hard to compile a table of the future positions of the planets.

In this very practical career, the moon poses a particularly thorny problem, that is, Newton's law attracts three stars. When we enter the 20th century, this problem will recur many times. Euler was the first person to put forward a computable solution (moon theory) to this moon problem. Three related stars are the moon, the earth and the sun. Although there is nothing to talk about this problem here, it will be pushed to the following chapters, but we can say that this problem is one of the most difficult problems in the whole mathematics category. Euler did not specifically answer this question, but his approximate calculation method (replaced by a better method today) has enough practical value to make the British calculator calculate the monthly table for the British Admiralty. For this, the calculator got 5,000 pounds (which was a considerable sum at that time), and Euler got a bonus of 300 pounds for his method.