Felix Klein biography

Felix Christian Klein is a German mathematician. He owns the idea of ​​algebraic classification of various sectors of geometry. The scientific career of Felix Klein initially developed as rapidly as no other in German history. He became an orderly professor, that is, he reached the top of the scientific hierarchy, when he turned only twenty -three years. At this age, many students still listen to lectures or only choose the head of their first doctoral work.

Klein printed a number of works on the solution of equations of the 5th, 6th and 7th degrees, on the integration of differential equations, about abele functions, and on non-evlide geometry. His works were printed mainly in the magazine Mathematische Annalen, whose editor he was along with Adolf Mair Klein's lecture was very popular, many of them were repeatedly reprinted and translated into many languages.

He also published several monographs on analysis, taking together the results achieved at that time. Even during the life of Klein, the three -volume of his collected works came out. Klein’s studies have a decisive effect on the further development of mathematics and physics. The famous German mathematician was elected a foreign member of the St. Petersburg Academy of Sciences, a member of the corr.

Berlin Academy of Sciences, he was a secret adviser and representative of the University of Gettingen in the upper house of the Prusia Parliament. Felix Klein was born on April 25, G. graduated from a gymnasium in Dusseldorf. He entered the Bonn University in the year. At first, Felix Klein planned to become a physicist. At this time, Julius Plykker was in charge of the department of mathematics and experimental physics in Bonn, and Klein became his assistant.

However, the main interest of the plugker was geometry. But in May, Professor Plucker suddenly died, leaving Klein without a leader and without a dissertation topic.

Klein himself set himself the task of geometry, continuing the subject of research of his late leader, and defended a doctoral dissertation in Bonn in December of that year. To continue education, Felix Klein chose a new leader - mathematics Alfred Klebsha him. Alfred Clebsch, Klebsh is known for many results in mathematical physics and algebraic geometry, but all his work is known to all mathematicians: Klebsh, together with Karl Neuman, created and edited the first numbers of the very respected scientific journal Mathematical Annals.

Just at the time when Felix Klein became one of the students of the famous mathematician Alfred Klebsha, he was appointed professor at the University of Gettingen. The student without hesitation followed his new teacher. Despite all the advantages of Gettingen, where Klein felt at home, he did not miss the opportunity to find out the world more and went to Berlin in the fall, then left for Paris in the year.

Staying in the French capital promised interesting results, but after two and a half months the idyll ended: in July, the war began between France and Prussia. Kleina as a subject of a hostile state was about to arrest, but he managed, showing considerable resourcefulness and quickness, crossing the Franco-German border in time and returning to Germany.

Klein met the New Year in Gettingen, where in January he defended his second doctoral work and received the title of privat-document. At that moment he was not yet twenty -two years old. For this period, there is a meeting with the Gettingen Professor Moritz Stern, friendship with which lasted many years. In the year, Klein becomes a professor at the University of Erlangen, on the recommendation of the famous mathematics of Klebsha.

Here he published his famous "Erlangen program." Klein's performance took place in December. The emphasis was on the need to show students the unity of science. Mathematical knowledge should be accompanied not only by natural science, but also by humanitarian information, so that the listeners have a common, multi -color picture of the world. Pure science should not be opposed to applied knowledge, mathematics should not evade the new tasks that physics and technology set before it.

Klein immediately acquired pan -European recognition. In Klein - a professor at the Higher Technical School in Munich. The famous scientist married Anna Hegel, the granddaughter of the famous philosopher. Together with Adolf Mayer, he became the editor -in -chief of the magazine Mathematische Annalen Felix Klein organized in Munich the so -called “mathematical circle”, where mathematicians and representatives of large industry and business were found.

The circle represented for its time a new form of scientific communication. Here, the directors of the tasks arising in real life met with theorists that these problems could solve. In the process of discussion, both parties came to a deeper understanding of the problem. In the year, the famous German scientist Felix Klein moved to the University of Leipzig. However, in the city of Klein he seriously fell ill due to overwork.

In the year, he took the position of professor of Gettingen University, where he worked until the end of his life.Klein led bright, deep and substantial optional courses in different subjects, from the theory of numbers to technical mechanics. Klein's lectures enjoyed exceptional success, he fascinated the listeners with scientific prospects and showed the romance and intrigue of mathematical research.

Listeners of his courses came to Gettingen from all countries and continents. At the beginning of the 20th century, Klein took an active part in the reform of school education, he is the author and initiator of a number of studies of the state of affairs with the teaching of mathematics in different countries. Klein contributed to the creation of a research institutes for applied research in a wide variety of technical fields at the University of Gettingen University.

Felix Klein participated in the publication of the complete works of Karl Friedrich Gauss and the first mathematical encyclopedia. Presented the University of Gettingen in parliament. Both in books and lectures, Klein tirelessly emphasized an important thought for him: mathematics should engage in not only the tasks that are born inside it, but to spread to all areas of knowledge, bringing the ideas of order there and forming the laws of real life in its universal language.

All his life, Klein tried to reveal internal ties between the individual branches of mathematics, as well as between mathematics, on the one hand, and physics and technology on the other. In the year, the lady of Klein was widely celebrated. The following year, the great mathematician died. One of the most important scientific achievements of Felix Klein was the first proof of the consistency of Lobachevsky's geometry.

To do this, he built her interpretation in the Euclidean space. Klein built an example of a one -sided surface - “Klein's bottle”. What is the "bottle of Klein"? The dream of a medieval alchemist is a mystical perfect hermetic vessel, where the external passes into the inner and internal into the external one, which contains itself and passes into itself, in which the internal and external parodoxically united all this resembles a snake, which has turned into a ring and swallowing its own tail.

To build a model of Klein’s bottle, it is necessary to take a bottle with two holes: in the bottom and in the wall, pull the neck, bend it down, and put it through the hole in the wall of the bottle for the real bottle of Klein in the four -dimensional space, but you cannot do without it in the three -dimensional Euclidean space, attach to the hole on the bottom of the bottle.

From the point of view of mathematics, the “bottle of Klein” is a closed that is, without a edge, a one -sided surface. And from the point of view of physics? How to imagine what the amazing "bottle" is similar to in reality? It turns out that it is impossible to build an absolutely correct model of this object in our three -dimensional world: a surface intersection will be observed here, which is completely absent in a four -dimensional dimension.

Conclusion: the true "bottle of Klein" can exist only in a four -dimensional dimension!