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Leonhard Euler

Leonhard Euler (1707 ~ 1783)

Profile of Leonhard Euler

Chinese name: Leonhard Euler

Foreign name: Leonhard Euler

Nationality: Switzerland

Place of birth: Switzerland

Date of Birth: April 15th, 1707

Died: September 18, 1783

Occupation: Mathematician, Physicist

Graduated from: University of Basel

Faith: Christianity

Main achievement: Creating symbols for functions

Create Analytical Mechanics

Solved the problem of the Seven Bridges of Konigsberg

Give various Euler formulas

Representative works: "Introduction to Infinite Analysis", "Principles of Differentials", "Principle of Integrals"

Astrological sign: Aries

IQ: 305

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Leonhard Euler -Swiss mathematician

Leonhard Euler (April 15, 1707-September 18, 1783), a Swiss mathematician and natural scientist. Born in Basel, Switzerland on April 15, 1707, and died in St. Petersburg, Russia on September 18, 1783. Euler was born to a priest's family and was influenced by his father since childhood. He entered the University of Basel at the age of 13, graduated from the university at the age of 15, and obtained a master's degree at the age of 16. Euler was one of the most prominent figures in mathematics in the 18th century. He not only contributed to the mathematics world, but also pushed the whole mathematics into the field of physics. He is the most prolific mathematician in the history of mathematics. He writes an average of more than 800 pages of papers each year. He also writes a lot of textbooks on mechanics, analysis, geometry, variational methods, etc., Introduction to Infinite Small Analysis, Differential "Principle of Learning" and "Principle of Integral Theory" have become classic works in the mathematical world. Euler's study of mathematics is so extensive that important constants, formulas, and theorems named after him are often seen in many branches of mathematics. In addition, Euler is also involved in the fields of architecture, ballistics, and navigation. Charles Kleiber, Swiss Secretary of State for Education and Research, once said: "Without the many scientific discoveries of Euler, we will live a completely different life today." French mathematician Laplace said: Reading Euler, he is Teacher for everyone. In 2007, to celebrate the 300th anniversary of Euler ’s birthday, the Swiss government, the Chinese Academy of Sciences and the Chinese Ministry of Education jointly held a commemorative event at the Documentation and Information Center of the Chinese Academy of Sciences in Beijing on the afternoon of April 23, 2007. The impact of modern life.

Biographies

Euler was born in Basel, Switzerland on April 15, 1707, and died in St. Petersburg, Russia on September 18, 1783. He was born to a priest family. At the age of 15, he received a bachelor's degree from the University of Basel and a master's degree the following year. In 1727, Euler came to Russia at the invitation of the St. Petersburg Academy of Sciences. In 1731 he succeeded Daniel Bernoulli as professor of physics. He devoted himself to research with great energy. During the 14 years in Russia, he did a lot of excellent work in analysis, number theory and mechanics. In 1741, he was invited to work at the Berlin Academy of Sciences by Prussian Frederick the Great for 25 years. During his time in Berlin, his research content was more extensive, involving planetary motion, rigid body motion, thermodynamics, ballistics, and demography. These work and his mathematical research promote each other. Euler's research on differential equations, surface differential geometry, and other mathematical fields during this period were groundbreaking. In 1766 he returned to St. Petersburg.

Euler was one of the most outstanding figures in mathematics in the 18th century. He not only made great contributions in mathematics, but also applied mathematics to almost the entire field of physics. He is again a prolific author. He has written a large number of textbooks on mechanics, analysis, geometry, and variational methods. "Introduction to Infinite Small Analysis", "Principles of Differentials", and "Principle of Integrals" have become classic works in mathematics. In addition to textbooks, his complete works have 74 volumes.

In the middle of the 18th century, Euler and other mathematicians founded the discipline of differential equations in the process of solving physical problems. It is worth mentioning that the first paper on the purely mathematical study of partial differential equations was "Research on the Integral Method of Equations" by Euler. Euler also studied the method of representing functions with triangular series, the series method of solving differential equations, and so on.

Euler introduced the parametric equation of the space curve and gave an analytical expression for the curvature radius of the space curve. In 1766 he published "Research on Curves on Surfaces" and established the theory of surfaces. This work is Euler's most important contribution to differential geometry and is a milestone in the history of differential geometry. Euler's contributions to analytics are endless. For example, he introduced the Γ function and B function, proved the addition theorem of elliptic integrals, the earliest introduced double integrals, and so on. The foundation of number theory as an independent branch of mathematics was laid by a series of achievements by Euler. He also solved the famous combinatorial problem: the Seven Bridges of Königsberg. Important constants, formulas, and theorems named after him are common in many branches of mathematics.

When he was young, he particularly liked mathematics, and started to teach Algebra by himself under the age of 10. This book has not even been read by some of his teachers. But Little Euler read it with interest, and when he didn't understand, he used a pen as a mark, and then asked others for advice afterwards. In 1720, the 13-year-old Euler was admitted to the University of Basel by his own efforts and was carefully instructed by Johann Bernoulli (1667-1748), the most famous mathematician at the time. This was a miracle at the time, and it once caused a sensation in the mathematical world. Euler Jr. is the university and the youngest student on the entire Swiss university campus.

Euler's profound knowledge, endless creative energy, and unprecedentedly rich writings are all amazing! He published his thesis from the age of 19 until the age of 76, and wrote a lot of books and papers for more than half a century. Up to now, you can see Euler's name in almost every field of mathematics, from Euler's line of elementary geometry, Euler's theorem of polyhedron, Euler's transformation formula of three-dimensional analytical geometry, Euler's solution of quartic equation to Euler in number theory. Pull functions, Euler's equations of differential equations, Euler's constants of series theory, Euler's equations of variational theory, Euler's formulas of complex variable functions, etc., are also countless. His contributions to mathematical analysis are more original, The book "Introduction to Infinite Small Analysis" is his landmark work, when mathematicians called him "the embodiment of analytics".

Euler is the most prolific mathematician in the history of science. According to statistics of his tireless life, he wrote a total of 886 books and papers, of which analysis, algebra, number theory accounted for 40%, geometry accounted for 18%, physics Harmonics accounted for 28%, astronomy accounted for 11%, and ballistics, nautical studies, and architecture accounted for 3%. The Petersburg Academy of Sciences has been busy for 47 years in order to organize his works.

Euler was a professor at the Petersburg Academy of Sciences and was one of the founders of the Berlin Academy of Sciences. He was the founder of rigid body mechanics and fluid mechanics, and the pioneer of the theory of elastic system stability. He believed that the differential equations of particle dynamics could be applied to liquids (1750). He used two methods to describe the motion of the fluid, namely the fluid velocity field according to the fixed point in space (1755) and the fluid mass point (1759). The former is called Euler method and the latter is called Lagrange method. Euler laid the theoretical foundation of the ideal fluid, and gave a continuous equation (1752) reflecting the conservation of mass and a fluid dynamics equation (1755) reflecting the law of momentum change. Euler has also written a lot on solid mechanics, such as the shape of the elastic pressure bar after instability, the vibration problem of the heavy chain suspended from the upper end, and so on. Euler has over 800 monographs and dissertations.

The asteroid Euler 2002 was named in honor of Euler.

Early years

Euler was born to a priest family in Basel, Switzerland. His father, Paul Euler, was a priest of the Christian Calvinist. Paul Euler studied theology at the University of Basel in his early years and later married a priest's daughter, Marg. Marguerite Brucker, Euler's mother. Euler is the eldest of their six children. Shortly after Euler was born, the family relocated from Basel to Lyon in the suburbs, where Euler spent most of his childhood.

Euler first came into contact with some mathematics from his father. Later, Euler moved back to Basel to live with his maternal grandmother, and began his formal studies there. In middle school, because Euler's school and Without teaching mathematics, he learned privately from a college student.

Euler entered the University of Basel at the age of 13, majoring in philosophy and law, but studied mathematics with Johann Bernoulli, then Europe's best mathematician, every Saturday afternoon. Euler obtained his master's degree in philosophy in 1723. The content of his dissertation is a comparative study of Cartesian and Newtonian philosophy. Later, Euler followed his father's wishes and entered the theology department, studying theology, Greek and Hebrew (Our's father wanted Euler to become a priest), but eventually John Bernoulli convinced Euler's father Allow Euler to learn mathematics and convince him that Euler is destined to be a great mathematician. In 1726, Euler completed his Ph.D. dissertation De Sono, which deals with the dissemination of sound. In 1727, Euler participated in an award-winning essay competition hosted by the French Academy of Sciences. The problem was to find out the optimal placement method of the mast on the ship. As a result, he won the second prize. The first prize was won by Pierre Bouguer, known as the "father of shipbuilding," but Euler later won the prize a total of 12 times in his life. First prize.

In Saint Petersburg

During this period, John Bernoulli's two sons, Daniel Bernoulli and Nicolas Bernoulli, worked at the Royal Academy of Sciences in St. Petersburg, Russia, and in Nicholas due to appendicitis After his death in July 1726 (just one year before he came to Russia), Daniel took over his position in the Institute of Mathematics / Physics and recommended Euler to replace his vacant post in the Physiology. Euler gladly accepted the invitation in November 1726, but did not immediately leave for St. Petersburg, but first applied for a professor of physics at the University of Basel, but with no success.

Euler arrived in St. Petersburg on May 17, 1727. At the request of Daniel et al., The Academy assigned Euler to the Institute of Mathematics / Physics, not the original Institute of Physiology. Euler maintains a close working relationship with Daniel and lives with Daniel. From 1727 to 1730, Euler also served as a Russian Navy medical officer.

The Russian Academy of Sciences was founded by Peter the Great in 1724. During the reign of Peter the Great and his successor, Queen Catherine, the Academy of Sciences was an attractive place for foreign scholars. The Academy of Sciences has sufficient funding sources and a large comprehensive library, and only enrolls very few students to ease the teaching burden of professors. The Academy of Sciences also attaches great importance to research, giving professors sufficient time and freedom to explore scientific issues.

Queen Catherine, also a patron of the Academy of Sciences, died on the day Euler arrived in St. Petersburg. Then Peter II succeeded, Peter II was a weak monarch, and the actual power was controlled by the Russian aristocracy. The aristocracy was wary of foreign scientists in the Academy of Sciences, so they cut off financial aid to Euler and his colleagues and troubled them in other ways.

The situation improved after the death of Peter II (1730). Euler quickly improved in the Academy of Sciences, and in 1731 was appointed professor of physics. Two years later, Daniel Bernoulli returned to Basel because he could not stand the censorship and hostility in St. Petersburg, and Euler replaced Daniel as the director of the Institute of Mathematics. In 1735, Euler also held a position at the Institute of Geography of the Academy of Sciences, assisting in the preparation of Russia's first map of the entire territory.

On January 7, 1734, Euler married the art teacher of the secondary school affiliated to the Academy of Sciences, the daughter of the Swiss Georg Gsell, Katharina Gsell (1707-1773). Has 13 children, of which only 5 live to adulthood.

In berlin

In view of the ongoing turmoil in Russia, Euler left St. Petersburg on June 19, 1741 to work at the Berlin Academy of Sciences, a post provided by Frederick II . He has lived in Berlin for 25 years and has written more than 380 articles there. In Berlin, he published two of his best-known works: An Introduction to Infinite Small Analysis on Functions, published in 1748; and An Introduction to Calculus, on differentiation, published in 1755. In 1755 he became a foreign member of the Royal Swedish Academy of Sciences.

Vision deterioration

Throughout Euler's mathematical career, his vision has been deteriorating. Three years after a near fatal fever in 1735, his right eye was almost blind, but he blamed it on his hard mapping work for the St. Petersburg Academy of Sciences. His vision continued to deteriorate during his stay in Germany, so much so that Frederick called him a "Cyclops". Euler's originally normal left eye later suffered from cataracts. A few weeks after he was diagnosed with cataracts in 1766, he was almost completely blind. Even so, the illness does not seem to affect Euler's academic productivity, which is probably due to his mental arithmetic ability and superior memory. For example, Euler can recite Virgil's epic Aeneas without hesitation, and can point out what the first and last lines of each page of the version he recites. With the help of the clerk, Euler's research in many fields has actually become more productive. In 1775 he completed an average math thesis every week.

Passed away

On September 18, 1783, after dinner, Euler was drinking tea and playing with her granddaughter. Suddenly, the pipe fell from his hand. He said, "My pipe," and bent down to pick it up, but he never stood up again, holding his head and saying, "I am dead." "Euler stopped computing and life." The latter sentence, often quoted by mathematical historians, comes from the French philosopher and mathematician Condorcet: "... il cessa de calculer et de vivre" (he ceased to calculate and to live).

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