Felix Klein isGermanymathematician。Born in Dusseldorf on April 25, 1849.He died in Gottingen on June 22, 1925.
Klein attended a high school in Dusseldorf. After graduation, he entered the University of Bonn to study mathematics and physics.He wanted to be a physicist, but the math professor Prick changed his mind.In 1868, Klein completed his doctoral thesis under the guidance of Professor Prick.In this year, Professor Prick died, leaving an unfinished basic geometry project. Klein was the best person to complete this task.Later Klein went to military service.In 1871, Klein acceptedGottingenInvited by the university to be a lecturer in mathematics.In 1872, he wasErlangenHe was only 23 when he was appointed as a professor of mathematics at the university.In 1875, heMunichThe College of Advanced Technology has obtained a teaching chair.1880~1886LeipzigUniversity professor.In 1886, Klein accepted the invitation of the University of Gottingen and came to Gottingen to start his career as a mathematician. He stayed here until his retirement in 1913.From 1872 to 1895, he was the chief editor of Gottingen Mathematics Yearbook, advocated editing the "Encyclopedia of Mathematics" and wrote the fourth volume of it.
Klein's first contribution to mathematics was discovered in cooperation with Li in 1870.They found outKummer Curvilinear on surfaceAsymptoteThe basic nature of.He further collaborated with Li to study the W-curve.In 1871, Klein published two papers on non Euclidean geometryproveIfeuclid geometry Is compatible, so is non Euclidean geometry.This puts non Euclidean geometry on the same solid foundation as Euclidean geometry.Klein's famousErlangen Program In, from the viewpoint of transformation group, the invariants and their spatial characteristics of various geometries are synthesized and classified according to this standard, thus unifying geometry.Today these views have become the standard for everyone.Transformation plays a major role in modern mathematics.Klein pointed out how to use transformation groups to express the basic characteristics of geometry.
And Klein thinks he's rightmathematicsThe main contributions offunctiontheoretically.In 1882, in a paper, he used geometric methods to deal with function theory and put potential theory and shape conservationmappingConnect.He also often uses physical concepts in function theory, especiallyfluid mechanics。
Klein comparedequationIn particular, we are interested in using transcendental methods to solve general equations of the fifth degree.stayErmettAfter cloning Nike and establishing a method similar to that of Briosch, Klein immediately tried to solve this problem with icosahedron group.This work led him to a series of papers onellipseResearch on modular function.
In 1884, Klein got an important relationship between algebra and geometry in his important work on icosahedron, and he developed the automorphic functionnumber theory。He and Robert Frick, a mathematician from LeipzigCo publishingA set of four volume works on automorphic functions and elliptic modular functions, which will influence the next 20 years.Another plan is to publish a setEncyclopaedia of Mathematics 。He actively participated in this work, editing the four volumes of mechanics with K. Muller.We will also mention Klein's bottle, a kind of surface with only one face.
Dynamics
Klein's contribution to mechanics is that he promoted the development of applied mechanics during his tenure in Gottingen.After visiting the International Fair in Chicago in 1893, Klein deeply felt the importance of basic disciplines for the development of industry.After his return to Germany, he made every effort to promote the application of mathematics, mechanics and other basic disciplines in engineering technology in Gottingen, and established the Department of Applied Mechanics in Gottingen University.In 1904, he recommended L. Plunt, who had studied engineering, as the dean of the department.This department is one of the birthplaces of modern mechanics.The school of modern mechanics represented by Plunt and T. von Carmen first grew and developed in the University of Gottingen, which was inseparable from Klein's efforts.Klein taught a wide range of courses in Gottingen, mainly on cross topics between mathematics and physics, such asDynamicsAnd potential theory.He realized that he wanted to rebuild Gottingen University as the worldMathematical researchThe importance ofcoreThe desire of.The famous mathematics magazine Mathematics Yearbook was managed by Klein to achieve and surpass the importance of Clare Magazine.This magazine focuses on complex analysis, algebraic geometry andInvariant theoryIt has a lot of characteristics.In practice analysis andgroup theoryNew areas are also outstanding.[1]
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Klein's works were compiled as Complete Works, a total of three volumes, published from 1902 to 1923.He and German physicist A. Sommerfeld co wrote 4 volumes of Gyro Theory, which was published from 1897 to 1903.
In 1885 Klein wasRoyal SocietyElected as a foreign member and awarded Copler Prize.
In 1908, Klein was elected by the International Mathematical Society as the President of the Conference of Mathematicians held in Rome.
Elementary Mathematics from a High Perspective was published by Fudan University Press. The author Klein wrote a popular reading of basic mathematics based on his lectures for German middle school mathematics teachers and students in Gottingen University for many years.This book reflects many of his views on mathematics and vividly shows people the legacy of first-class masters. After its publication, it was translated into many languages. It is an immortal masterpiece of mathematics education and has an enduring influence.The book is divided into three volumes.Volume I: Arithmetic
