Obsessed with mathematics and diligent in study, at the age of 18, Gauss invented the method of making regular 17 polygons with compasses and straightedge, thus solving the problem that has not been solved since 2000. 2/kloc-graduated from university at the age of 0, and received his doctorate at the age of 22. In his doctoral thesis, he proved the basic theorem of algebra, that is, the unary n-degree agenda must have roots in the complex number range. In geometry, Gauss is one of the inventors of non-Euclidean geometry. Gauss's most important contribution is number theory. His magnum opus Arithmetic Research marks that number theory has become an independent branch of mathematics, and the content discussed in this book has become the research direction of number theory until the 20th century. Gauss first used congruence notation, and systematically expounded the theory of congruence formula. He proved important results in number theory, such as the law of quadratic reciprocity. After the death of Gauss, people built a Gauss image on the basis of a regular 17 prism to commemorate this great mathematician.
1777 was born in a craftsman's family in Brunswick on April 30th, and 1855 died in Gottingen on February 23rd. When he was a child, his family was poor, but he was extremely clever. Before he entered the school for education, he was sponsored by a noble. From 1795 to 1798, I studied at the University of G? ttingen, and 1798 transferred to Helmstadter University. The following year, he received his doctorate for proving the basic theorem of algebra. From 1807, he served as a professor at the University of G? ttingen and director of the G? ttingen Observatory until his death. Gauss is one of the founders of modern mathematics, and he has a great influence in history. He can be juxtaposed with Archimedes, Newton and Euler, and is known as the "prince of mathematics". Gauss's achievements cover all fields of mathematics, and he has made pioneering contributions in number theory, non-Euclidean geometry, differential geometry, hypergeometric series, complex variable function theory, elliptic function theory and so on. He attached great importance to the application of mathematics, and emphasized the use of mathematical methods in the research of astronomy, geodesy and magnetism.
Gauss has been engaged in mathematics for a long time, and applied mathematics to physics, astronomy and geodesy, with rich writings and many achievements. In his life, he published 323 works, put forward 404 scientific ideas (publication 178) and completed four major inventions: (sunlight), reflector (1820), photometer (182 1) and telegraph. The main achievements in various fields are: 1. In physics and geomagnetism, we study electrostatics (such as Gauss theorem), thermoelectric and triboelectricity, measure non-mechanical quantities (such as magnetic field intensity) by using the absolute unit (length, mass and time) rule, and study the theoretical distribution of geomagnetic field (such as spherical harmonic analysis of magnetic potential at any point on the ground). 2. Using geometry knowledge to study paraxial ray behavior and imaging of optical system, and establish Gaussian optics. 3. Astronomy and geodesy, such as the calculation of asteroid orbit, theoretical research on the size and shape of the earth, etc. 4. Combined with the measurement of experimental data, the probability and statistics theory and error theory are developed, the least square method is invented and the Gaussian error curve is introduced. In addition, in pure mathematics, he strictly proved some basic theorems of number theory, algebra and geometry, such as the product theorem of natural numbers as prime numbers, binomial theorem, divergence theorem and so on.
occupation
He showed superhuman mathematical genius when he was young. 1795 entered the University of G? ttingen. The next year, he discovered the regular drawing of regular heptagon. The condition that a ruler can be used as a regular polygon is given, and the unsolved problem since Euclid is solved.
Gauss's mathematical research covers almost all fields and has made pioneering contributions in number theory, algebra, non-Euclidean geometry, complex variable function, differential geometry and so on. He also applied mathematics to the study of astronomy, geodesy and magnetism, and invented the principle of least square method. Korea's research on number theory was summarized in Arithmetic Research (180 1), which laid the foundation of modern number theory. It is not only an epoch-making work in number theory, but also one of the rare classic works in the history of mathematics. Gauss's important contribution to algebra is to prove the basic theorem of algebra, and his existence proof opens up a new way of mathematical research. Gauss got the principle of non-Euclidean geometry around 18 16. He also deeply studied the complex variable function, established some basic concepts and discovered the famous Cauchy integral theorem. He also discovered the double periodicity of elliptic functions, but these works were not published before his death. 1828, Gauss published "General Theory of Surfaces", which comprehensively and systematically expounded the differential geometry of spatial surfaces and put forward the theory of intrinsic surfaces. Gaussian surface theory was later developed by Riemann. Gauss published 155 papers in his life. He is very strict with his studies and only publishes what he thinks is mature. His works include the concept of geomagnetism and the law of universal gravitation. Repulsion is inversely proportional to the square of distance.
Gauss's most famous story is that when he was ten years old, the primary school teacher gave an arithmetic problem: "Calculate 1+2+3 …+ 100 =?" . This is difficult for beginners of arithmetic, but Gauss solved the answer in a few seconds. He used the symmetry of arithmetic progression (arithmetic progression) and then put the numbers together like a general arithmetic progression sum: 1+ 100, 2+99, 3+98, ... 49+52. In 180 1 year, Gauss On New Year's Day that year, a celestial body named Ceres was discovered, which was later proved to be an asteroid. At that time, it seemed to be approaching the sun. Although astronomers have 40 days to observe it, they can't calculate its orbit. After only three observations, Gauss proposed a method to calculate the orbital parameters, and the accuracy achieved enabled astronomers to reposition Ceres at the end of 180 1 and the beginning of 1802 without any difficulty. In this calculation method, Gauss used the least square method he created in about 1794 (a method that can get the best estimate from the minimum sum of variance in a specific calculation), and this method was recognized in astronomy. The method described in his celestial motion theory is still used today, and it can meet the requirements of modern computers with a little modification. Gauss achieved similar success on the asteroid "Pallas Athena".
Mathematical genius
There are occasional prodigies in history. Prodigies often appear in mathematics, music, chess and other fields. C.F.Gauss, a mathematical genius, is the best among all kinds of geniuses. Just as the lion is called the king of beasts, Gauss is the king of mathematicians. He has a nice name-Prince of Mathematics. Gauss is not only recognized as the greatest mathematician in19th century, but also as the three greatest mathematicians in history with Archimedes and Newton. Now the names of Archimedes and Newton have already entered the middle school textbooks, and their work has more or less become common sense, while Gauss and his mathematics are still out of reach, even in the basic courses of universities. However, the portrait of Gauss is impressively printed on the German paper 10 mark with the largest circulation, and George Washington and Elizabeth II appear on the US dollar and the British pound respectively. 1777 On April 30th, Gauss was born in Brunswick, Lower Saxony, Germany. No one in his ancestors can explain why Gauss is such a genius. Gauss's father was an ordinary laborer who worked as a stonemason, tracker and gardener. His mother, his father's second wife, is a maid and has no education, but she is smart, kind, humorous and has a strong personality. She died at the age of 97, and Gauss was her only adopted son. It is said that Gauss discovered a mistake in his father's book when he was three years old. When Gauss was 9 years old, he was studying in a public elementary school. Once, his teacher asked his students to add up the numbers 1 to 100. Gauss put the slate face down on his desk almost immediately. When all the slates were finally turned over, the teacher was surprised to find that only Gauss got the correct answer: 5050, but there was no calculation process. Gauss has summed up this arithmetic progression in his mind. He noticed that1+100 =1kloc-0/,2+99 =1kloc-0/,3+98 =1. In his later years, Gauss often humorously claimed that he could calculate before he could speak, and said that he asked adults how to pronounce letters, so he learned to read. Gauss's precocity attracted the attention of the Duke of Brunswick, who was an enthusiastic patron. Gauss/Kloc-entered Brunswick College at the age of 0/4, and/Kloc-entered the University of G? ttingen at the age of 0/8. At that time, Gottingen was still unknown, and the arrival of Gauss made this world-famous university play an important role in the future. At first, Gauss hesitated between becoming a linguist and a mathematician. It was on March 30th 1796 that he decided to devote himself to mathematics. At the age of 19, he made amazing contributions to the Euclidean drawing theory of regular polygons (using only compasses and scaleless rulers). In particular, he discovered the method of making regular heptagon, which is a mathematical unsolved case with a history of more than two thousand years. Gauss has been in full swing since he was a rookie, and has maintained this level for the next 50 years. Gauss lived in the era of German romanticism. Influenced by fashion, Gauss is full of beautiful words in his personal letters and stories. Gauss said: "Mathematics is the queen of science, and number theory is the queen of mathematics." People in that era also called Gauss "the prince of mathematics". In fact, throughout Gauss's life's work, it seems to be romantic.
In Gauss's time, few people could share his ideas or provide him with new ones. Whenever he discovers a new theory, he has no one to discuss. This sense of loneliness, accumulated over time, caused his aloof indifference. This intellectual loneliness has only been experienced by a few great men in history. Gauss never takes part in public debates. He always hates arguing. He thinks it is easy to turn into a stupid cry, which may be a psychological resistance to his rude and autocratic father since he was a child. Gauss rarely left G? ttingen after becoming famous, and repeatedly refused invitations from Berlin and St. Petersburg Academy of Sciences. Gauss even hates teaching and is not keen on cultivating and discovering young people. Naturally, it is impossible to build any schools. This is mainly due to Gauss's outstanding talent, so he is lonely inside. But this does not mean that Gauss has no outstanding students. Riemann sum Dirichlet was a great mathematician, and Detkin and Eisenstein also made outstanding contributions to mathematics. But because of the peak of Gauss, among these people, only Riemann (who succeeded Gauss after Dirichlet's death) is considered close to Gauss. Jacoby and Abel, great mathematicians of Gauss's contemporaries, complained that Gauss neglected their achievements. Jacoby is a thoughtful man. He has a famous saying that has been passed down to this day: "The only purpose of science is to add luster to the human spirit." He is a compatriot of Gauss and Dirichlet's father-in-law, but he has never been able to reach a close friendship with Gauss. 1849 At the celebration in G? ttingen, jacoby, who came from Berlin, sat on the honor seat next to Gauss. When he wanted to find a topic to talk about mathematics, Gauss ignored it. This may be the wrong time. At that time, Gauss had a few glasses of liqueur, and he was a little uncontrollable. But even on another occasion, I'm afraid the result is the same. In a letter to his brother about the banquet, jacoby wrote, "You know, in these twenty years, he (Gauss) never mentioned me and Dirichlet ..." Abel's fate was tragic. Like his later compatriots Ibsen, Greg and Monk, he is the only Norwegian who has made worldwide achievements in his field. He is a great genius, but he lives in poverty and knows nothing about his contemporaries. When Abel was 20 years old, he solved a big problem in the history of mathematics, that is, he proved that it is impossible to solve the general quintic equation with roots. He sent some famous mathematicians in Europe a short six-page "insoluble" proof, and Gauss naturally received one. Abel was full of confidence in his introduction, thinking that mathematicians would accept this paper in good faith. Soon, Abel, the son of a country priest, started the only hiking trip in his life. He wanted to use this article as a stepping stone at that time. Abel's greatest wish on this trip is to visit Gauss, but Gauss is out of reach. He just browsed a few lines, then put it aside and continued to concentrate on his research. On the journey from Paris to Berlin, Abel had to bypass Gottingen with increasing pain. Although Gauss is aloof and arrogant, it is surprising that he has been living a well-off middle class life without being hit by the cold reality. This kind of blow is often mercilessly imposed on everyone who lives out of the real environment. Perhaps Gauss's pragmatic and perfect personality helps him to grasp the simple reality in life. Gauss received his doctorate at the age of 22, was elected as a foreign academician of St. Petersburg Academy of Sciences at the age of 25, and was appointed as a professor of mathematics and director of the Observatory at the age of 30. Although Gauss doesn't like flashy glory, in the fifty years after he became famous, these things fell on him like raindrops, and almost all of Europe was involved in this wave of awards. He won 75 honors in his life, including "Senator" awarded by King George III of England 18 1845, and 1845. Gauss's two marriages were also very happy. After his first wife died in childbirth, Gauss married his second wife in less than ten months. There is a common phenomenon in psychology and physiology. People who have a happy marriage often remarry soon after losing their spouse, and so does johann sebastian bach, a musician who has been down and out all his life.