Chinese name: Felix Klein mbth: Felix Christian Klein alias: Klein Nationality: German birthplace: Dü sseldorf, Germany Date of birth:1April 25th, 849 Date of death: 192 5 Occupation: Graduate School of Mathematicians. The main achievement of Bonn University: the masterpiece of non-Euclidean geometry, group theory and function theory: elementary mathematics with high viewpoint. Life, major achievements, mathematics, mechanics, work honor, life of characters Felix Klein is a German mathematician. Born in Dü sseldorf on April 25th, 1849. 1925 died in gottingen on June 22nd. Klein goes to middle school in Dü sseldorf. After graduation, he was admitted to Bonn University to study mathematics and physics. He originally wanted to be a physicist, but Pruck, a professor of mathematics, changed his mind. From 65438 to 0868, Klein completed his doctoral thesis under the guidance of Professor Pruck. This year, Professor Pruck passed away, leaving an unfinished geometric foundation project. Klein is the best person to finish the task. Klein later went to do military service. 187 1 year, Klein accepted the invitation of the University of G? ttingen as a mathematics lecturer. 1872, he was hired as a professor of mathematics by Herun University, when he was only 23 years old. 1875, he got a position in Munich Institute of Advanced Technology. University of Leipzig professors range from 1880 to 1886. 1886, Klein accepted the invitation of the University of G? ttingen and came to G? ttingen to start his career as a mathematician. He stayed here until 19 13 retired. From 1872 to 1895, he was the editor-in-chief of the Gottingen Mathematical Yearbook, advocated the editing of the Encyclopedia of Mathematics and compiled the fourth volume. His main topics are non-Euclidean geometry, group theory and function theory. The publication of his "Irish Root Program" (1872 lecture by full professor of Herun Root University) classified all kinds of geometry according to their basic transformation groups, which had a far-reaching impact: it was the synthesis of mathematical contents at that time. His works include elementary mathematics from a high perspective. The main achievement of Klein's first contribution to mathematics was discovered in cooperation with Li in 1870. They discovered the basic properties of the asymptote of the curve on the Cuomo surface. He further cooperated with Li to study the W curve. 187 1 year, Klein published two papers on non-euclidean geometry, which proved that if euclidean geometry is compatible, then non-euclidean geometry is also compatible. This puts non-Euclidean geometry on the same solid foundation as Euclidean geometry. In his famous Herun root program, Klein synthesized various geometric invariants and their spatial characteristics from the point of view of transformation groups, and classified them into standards, thus unifying geometry. Today, these views have become everyone's standard. Transformation plays an important role in modern mathematics. Klein pointed out how to express the basic characteristics of geometry with transformation groups. Klein himself thinks that his contribution to mathematics is mainly in function theory. 1882, he used geometric method to deal with function theory and conformal mapping to connect potential theory. He also often applies physical concepts to functional theory, especially fluid mechanics. Klein is interested in equations greater than quartic, especially in solving general equations with quintic by transcendental method. After Hermite and Cloneker established a method similar to Brioski, Klein immediately tried to solve this problem completely with icosahedron. This work led him to study elliptic module functions in a series of papers. 1884, Klein obtained the important relationship between connected algebra and geometry in his important book about icosahedron, and he developed the theory of automorphism function. He and Robert Frick, a mathematician from Leipzig, jointly published a set of four-volume works on automorphism function and elliptic module function, which influenced the next 20 years. Another plan is to publish an encyclopedia of mathematics. He took an active part in this work and edited four volumes of Mechanical Part with K. Mill. We should also mention Klein's bottle, a curved surface with only one face. Mechanical Klein's contribution to mechanics is that he promoted the development of applied mechanics during his tenure at Gottingen. Klein visited the Chicago International Expo on 1893, and deeply felt the importance of basic disciplines for industrial development. After returning to Germany, he tried his best to promote the application of basic disciplines such as mathematics and mechanics in engineering technology in G? ttingen, and established the Department of Applied Mechanics at the University of G? ttingen. 1904 he recommended L. Pelant, an engineering student, as the dean. This department is one of the cradles of modern mechanics. The modern school of mechanics, represented by Pelant and T. von Carmen, first developed and expanded in the University of G? ttingen, which is inseparable from Klein's efforts. Klein teaches a wide range of courses in G? ttingen, mainly the interdisciplinary topics between mathematics and physics, such as mechanics and potential theory. He realized his wish to rebuild the University of G? ttingen into an important mathematical research center in the world. It is under the management of Klein that the famous mathematical magazine Mathematical Yearbook can reach and surpass Claire Magazine in importance. This magazine features complex analysis, algebraic geometry and invariant theory. It is also excellent in new fields such as real analysis and group theory. Works Honors Klein's works have been compiled into The Complete Works, with a total of 3 volumes, published in 1902 ~ 1923. He and the German physicist A. Sommerfeld co-authored the four-volume Gyro Theory, which was published in 1897 ~ 1903. 1885 Klein was elected as a foreign member of the Royal Society and awarded the Coppler Award. 1908 Klein was elected as the president of the congress of mathematicians held in Rome by the International Mathematical Society.