The story of a mathematician

Euler (L.Euler,1707.4.15-1783.9.18) is a Swiss mathematician. Born in Basel, Switzerland, died in Petersburg. Father Paul Euler is a priest and likes mathematics, so Euler has been influenced by this since he was a child. But his father insisted that he study theology in order to take over his class in the future. Fortunately, Euler didn't take the road arranged by his father. My father went to school in university of basel, and he worked with famous mathematicians at that time (johann bernoulli,1667.8.6-1748.1) and Jacob Bernoulli (1654.6438+02.27-). Because of this relationship, Euler got to know John's two sons: Nicolaus Bernoulli (1695- 1726) and daniel bernoulli (1700.2.9-1782.3.60000000606), who are good at mathematics. All these have benefited Euler a lot. 1720, Euler, who was only 13 years old, became a student in university of basel, and John carefully cultivated the clever Euler. When John found that the knowledge in the classroom could not satisfy Euler's thirst for knowledge, he decided to give him lessons, answer questions and teach alone every Saturday afternoon. John's hard work was not in vain. Under his strict training, Euler finally grew up. 17 years old, became the first young master in the history of Basel and became John's assistant. Under the guidance of John, Euler chose the way of mathematical research by solving practical problems from the beginning. 1726, 19-year-old Euler won the support of the Paris Academy of Sciences for writing on ships with masts. This indicates that Euler's feathers are plump and he can spread his wings and fly from now on.

Euler's growth is inseparable from his history. Of course, there is another important factor in Euler's success, and that is his amazing memory! He can recite the first 10 powers of the first 100 prime numbers, the epic Egnel by the Roman poet Virgil, and all the mathematical formulas. Until his later years, he was able to repeat all his notes from his youth. He can recite the calculations of advanced mathematics.

Although his talent is very high, it is hard to imagine the result without John's education. Because johann bernoulli, with his rich experience and profound understanding of the development of mathematics, can give important guidance to Euler, and let him learn books that are difficult to learn but necessary at the beginning, and avoid many detours. This history had a great influence on Euler, so that after he became a great scientist, he still did not forget to educate new people, which was mainly reflected in writing textbooks and directly cultivating talented mathematicians, including Lagrange (J.L. Lagrange,1736.655438+0.25-1813.4). 46666

Euler himself is not a teacher, but he has a greater influence on teaching than anyone else. As a world-class scholar and professor, he shoulders the heavy responsibility of solving profound problems, but he can ignore the criticism of "celebrities" and be enthusiastic about the popularization of mathematics. He had a profound influence on the introduction of infinitesimal analysis, differential method and integral method. Some scholars believe that since 1784, elementary calculus and advanced calculus textbooks have basically copied Euler's books, or copied those books from Euler. In this respect, Euler is different from Gauss (C. F. Gauss,1777.4.30-1855.2.23) and Newton (I. Newton,16438+0.4-65438+588). He published a large number of well-known articles in German, Russian and English, and also compiled a large number of textbooks for primary and secondary schools. His textbooks on elementary algebra and arithmetic are well thought out and well described. He used many new narrative methods to make these books both rigorous and easy to understand. Euler first defined logarithm as the inverse operation of power, and discovered for the first time that logarithm has infinite values. He proved that any nonzero real number r has infinite logarithm. Euler made trigonometry a systematic science. He first gave the definition of trigonometric function by ratio, but he always used the length of line segment as the definition before. Euler's definition makes trigonometry jump out of the circle of studying triangular tables only. Euler analyzed and studied the whole trigonometry. Before that, every formula was only derived from the chart, and most of them were expressed by narration. Euler analytically deduced all the triangular formulas from the first few formulas, and got many new formulas. Euler used A, B and C to represent the three sides of a triangle, and A, B and C to represent the angle opposite to the first side, thus greatly simplifying the narrative. Euler's famous formula:

Trigonometric function is related to exponential function.

In the popularization of education and scientific research, Euler realized that the simplification and regularization of symbols not only contributed to students' learning, but also contributed to the development of mathematics, so Euler created many new symbols. Such as sin, cos, etc. Are used to represent trigonometric functions, e is used to represent the base of natural logarithm, f(x) is used to represent functions, sigma is used to represent summation, and I is used to represent imaginary numbers. Pi π was not initiated by Euler, but only became popular at the initiative of Euler. Moreover, Euler unified e, π and I in an amazing relationship. Euler introduced Euler constant c when studying series, which is another important number after π and e.

Euler not only attaches importance to education, but also attaches importance to talents. At that time, Lagrange in France was only 19 years old, while Euler was 48 years old. Lagrange and Euler exchanged views on the "isoperimetric problem", and Euler was also studying this problem. Later, Lagrange made achievements, and Euler suppressed his paper and let Lagrange publish it first, which made him famous.

Euler didn't find a suitable job in Switzerland when he graduated from university at the age of 19. 1in the spring of 727, he tried to be the director of the teaching and research section in Basel, but failed. At that time, the Russian Academy of Sciences in St. Petersburg had just been established and was recruiting scientists and talents all over the country. Daniel bernoulli, who had applied to work in Petersburg, knew Euler's talent, so he tried his best to hire Euler to go to Russia. In this case, Euler left his motherland. Due to Daniel's recommendation, Euler was invited to St. Petersburg as Daniel's assistant on 1727. In St. Petersburg Academy of Sciences, he successfully obtained the position of associate professor of advanced mathematics. 173 1 was appointed as the director of the teaching and research section of theoretical physics and experimental physics. 1733, Euler, who was only 26 years old, replaced Daniel who returned to Switzerland and became a professor of mathematics and the head of the mathematics department of Petersburg Academy of Sciences.

During this period, Euler worked hard and published a large number of excellent mathematical papers, as well as other papers and works.

The foundation of classical mechanics was laid by Newton, and Euler was its main architect. 1736, Euler published "Mechanics, or the Theory of Analytically Describing Motion", in which he clearly put forward the concept of particle or particle for the first time, studied the velocity of particle moving along any curve for the first time, and applied the concept of vector to problems related to velocity and acceleration.

At the same time, he founded analytical mechanics and rigid body mechanics, and studied and developed elasticity theory, vibration theory and material mechanics. He applied vibration theory to music theory. 1739 published a book on music theory. 1738, the French Academy of Sciences set up a paper prize to answer the essence of heat, and Euler's article on fire won the prize. In this article, Euler regards the essence of heat as the vibration of molecules.

The most striking feature of Euler's research problem is that he extended his hand to the deep layer of nature and society. He is not only an outstanding mathematician, but also a master of integrating theory with practice and applying mathematics. He likes to study specific concrete problems, unlike some modern mathematicians who are tired of studying general theories.

It is precisely because the problems studied by Euler are closely related to the actual production, social needs and military needs at that time that Euler's creative talents have been fully exerted and amazing achievements have been made. While doing scientific research, Euler also applied mathematics to practice, which solved many scientific problems for the Russian government and made important contributions to society. For example, the renovation plan of the Fino Canal, the design and approval of drainage facilities in Gong Yan, the compilation of school textbooks and the government's help in drawing maps; During my work in the Weights and Measures Committee, I participated in the research on the accuracy of various weighing instruments. In addition, he also wrote comments for the publications of the Academy of Sciences and chaired the work of the Committee for a long time. He not only did a lot of work for the Academy of Sciences, but also took time to give lectures in universities, give public speeches and write popular science articles, providing astronomical data for meteorological departments and assisting construction units in mechanical analysis of design structures. 1735, Euler set out to solve an astronomical problem-calculating the orbit of comets (this problem requires the efforts of several famous mathematicians for several months). Because Euler used a new method invented by himself, it only took three days. However, three consecutive days of fatigue also made Euler break down from constant overwork, and the disease made Euler, who was only 28 years old, blind in his right eye. Such a disaster did not make Euler yield. He is still obsessed with science and works selflessly. However, due to the long-term power struggle of the Russian ruling group, it has increasingly affected Euler's work and made Euler very depressed. As it happens, Prussian King frederick the great (reign time 1740- 1786) learned about Euler's situation and invited him to Berlin. Although Euler loved his second hometown very much (where he worked and lived in Tapp in 14), he left St. Petersburg Academy of Sciences temporarily in 174 1 and took a position in Berlin Academy of Sciences as the director of the Institute of Mathematical Physics. 1759 became the leader of Berlin Academy of Sciences. While working in Berlin, he didn't forget Russia. He instructed his students in Russia through letters and sent his scientific works to Russia, which played a great role in the development of Russian science.

During his work in Berlin, he successfully applied mathematics to other scientific and technological fields and wrote hundreds of papers. Many important achievements in his life were made during this period. For example, the influential Introduction to Differential Analysis and Principles of Differential Calculus were published during this period. In addition, he also cooperated with D'Alembert (I.L.R.D 'Alembert,1717.1.16-1783./kloc-0. In Euler's time, there was no distinction between pure mathematics and applied mathematics. For him, the whole physical world is where his mathematical methods come into play. He studied the motion properties of fluid, established the basic differential equation of ideal fluid motion, published papers such as Principles of Fluid Motion and General Principles of Fluid Motion, and became the founder of fluid mechanics. He not only applied mathematics to natural science, but also applied the achievements of one discipline to another. For example, he applied his basic equation of ideal fluid motion to the flow of human blood, thus increasing his contribution to biology. On the basis of fluid mechanics and tidal theory, he enriched and developed the theory of ship design, manufacture and navigation, published a book "Navigation Science", and won the Paris Academy Award for his article "On the Left and Right of Ships". Not only that, he also solved many practical social problems for Prussia. From 1760 to 1762, Euler sent letters to Princess Charlotte on philosophy, physics, cosmology, theology, chemistry and music at the invitation of the prince. These communications fully reflect Euler's profound knowledge, high literary accomplishment and philosophical accomplishment. Later, these communications were compiled into a letter to a German princess, which was published in three volumes in 1768. Translations from all over the world are very popular and become a story for a while.

Since Euler 174 1 left Petersburg, the political situation in Russia has been bad, and the regime has changed several times, and finally it fell into the hands of Catherine II. Drawing lessons from the past, she began to devote herself to literary martial arts. While communicating with French enlightenment scholars such as Voltaire and Diderot, she also recruited influential scientists to serve in the Petersburg Academy of Sciences. Euler naturally became the main target of her employment. 1766, Euler was invited back to Petersburg, and this time Russia prepared superior working conditions for him.

At this time, Euler's scientific research work has been fruitful, and his thoughts are becoming more and more mature. Apart from some special topics, he hopes to make a systematic summary of past achievements in his later years and publish several high-quality works. However, bad luck came to him again. Due to the cold climate in Russia and the fatigue of work, Euler's left eye went blind again, and from then on, Euler fell into the darkness where he could not see his fingers. But Euler is very strong. He insists on writing by dictation and other people's records. He first focused on the book Principles of Calculus. In this three-volume masterpiece, Euler systematically expounds all the achievements since the invention of calculus, and is full of Euler's incisive insights. 1768, the first volume of Integral Principle was published in St. Petersburg. The third volume was published in 1770. In the same year, he wrote a complete Introduction to Oral Algebra, which was published in Russian, German and French and became a textbook for generations in Europe. Just as Euler was fighting in the dark, bad luck came again. 177 1 year, a fire in St. Petersburg surrounded Euler and his house with seedlings. At this critical moment, it was a servant who risked his life to carry Euler out of the fire. Although Euler survived, his books and a lot of research results were reduced to ashes. All kinds of hardships did not bring Euler down. Immediately after the fire, he devoted himself to new creation. The information was burned, and he was blind. In this case, he recalled his research with his strong will and amazing perseverance. Euler's memory is really hard to get. He can recite the notes from decades ago completely, and the mathematical formula is of course more fluent. Euler always thought carefully about the reasoning process, and then his eldest son dictated and recorded it. In this way, he published more than 400 papers and several monographs, accounting for almost half of all his works. 1774, he concentrated his achievements in studying variational problems for many years and published a book, Skills of Finding Curves with Some Maximal or Minimal Properties. Therefore, a new branch variational method came into being. In addition, Euler also studied the "three-body problem" in astronomy, such as the movement and transportation of the moon. Later, he solved Newton's unsolved problem of the moon's motion and created an accurate theory of the moon's motion around the earth. In order to make better astronomical observation, he studied optics, astronomical telescope and microscope. This paper studies the phenomenon of light passing through various media and the related color separation effect, puts forward complex objective principles, and publishes a monograph on optical instruments, which has made a pioneering contribution to the design and calculation theory of telescopes and microscopes. 177 1 published a concluding work, Refractive Optics. Euler started writing at the age of 19 until his death, leaving a lot of papers and works. Even after his death, many manuscripts he left behind enriched the Journal of St. Petersburg Academy of Sciences in the last 47 years. As far as scientific research results are concerned, Euler is second to none in both the history of mathematics and the history of natural science.

As such a scientific giant, he is not a dull person in life. He is gentle, cheerful and sociable. Euler was married twice and had 13 children. He loves family life and often plays science games and tells stories with children.

Euler's vigorous energy and research spirit persisted until the last moment of his life. 1On the afternoon of September, 783, Euler was playing with his little granddaughter while thinking about calculating the trajectory of Uranus. Suddenly, he slipped down from his chair and whispered, "I'm dead." A master of science thus ended his life.

In history, there are not many people who can compare with Euler. Some historians list Euler, Archimedes, Newton and Gauss as the four greatest mathematicians in history. The reason is that they all have one thing in common, that is, while creating pure theories, they also apply these mathematical tools to solve a large number of practical problems in astronomy, physics and mechanics. Their work is interdisciplinary, and they constantly absorb rich nutrition from practice, but they are not satisfied.

Because of Euler's outstanding work, later famous mathematicians spoke highly of Euler. Laplace, a great mathematician (1749.3.23-1827.3.5) said, "Read Euler, this is the teacher of all of us." Diego, known as the prince of mathematics, also said: "The study of Euler's works will still be the best school in different fields of mathematics, and nothing can replace it."