Klein blue also stands for loneliness.

Ha ha. I found it online. You can try to adjust it.

Introduction to Klein:

Klein (1849 ~ 1925)

Christian Felix Klein

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 project on basic geometry. 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. Here, his students include leonid hurwicz, Von Dyke, Loen, Planck, Bianchi and Ricky. Five years later, Klein was invited to teach geometry at the University of Leipzig. Here, he became colleagues with his outstanding students, such as Von Dyke, Loen, Stuart and Engel.

1886, Klein accepted the invitation of the University of G? ttingen and came to G? ttingen to start his career as a mathematician. He teaches a wide range of courses, mainly interdisciplinary topics between mathematics and physics, such as mechanics and potential theory. He stayed here until 19 13 retired. 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.

It is difficult to understand the characteristics of Klein's contribution to geometry, because even with most of our mathematical thoughts today, it is difficult to understand the novelty of his results.

Klein's first contribution to mathematics was discovered in collaboration 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 perspective 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 enabled him to study elliptic module functions in a series of papers.

1884, Klein got the important relationship between 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 mechanics with K. and Mill. We should also mention Klein's bottle, a curved surface with only one face.

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.