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David Gilbert

Picture of David Gilbert

Date of Birth: 01/23/1862

Age: 81

Place of birth: Wehlau

Citizenship: Germany

Background

In February 1885 Gilbert defended his doctoral thesis On a basis in the space of invariants, and in May at the insistence of Hurwitz went to Leipzig, where he attended lectures by Klein and involved in his workshop. In March 1886, on the advice of the Klein went to a seminar in Paris, where he listened to the lecture of Poincare, Picard, Hermite, Jordan. When he returned to Konigsberg, Hilbert introduced gabilitatsionnuyu theses and gave a lecture at the Faculty, and then received the title of professor and to lecture at the university.

A special feature of scientific work Hilbert is that it can be divided into several periods, each of which he was engaged in only one of the tasks of the field, and then immersed in a different area. The period from 1885 to 1893 devoted to the theory of invariants. This has significantly advanced the field of mathematics, he proved the main theorem on the existence of a finite basis in the ring of invariants. The continuation of this research was the work on the theory of abstract fields, rings and modules, covering virtually the modern algebra. The works of Hilbert on the theory of invariants drawn a line under this area of ??mathematics, and he moved on to a new topic, the theory of algebraic number fields.

In March 1895, supported by Klein, Hilbert received a professorship of the University of Gottingen. Soon the German Mathematical Society invited him to write an overview of the theory of numbers. While working on the review, Gilbert systematized this most difficult area of ??mathematics, combined all known results in rigorous theory. In one of the reviews of this work spoke about her as "the inspired work of art", and the introduction has been called "one of the best possessions of German prose." A year after the appearance of the review, in 1898, he published a work of Hilbert`s theory of relative Abelian fields in which he gave an outline of the theory of class fields, and then engaged in another area - the foundations of geometry.

Gilbert brought the axioms of geometry to perfection, giving a sample of the completed statement of a mathematical discipline. Choosing a system of axioms, is slightly different from the axioms of Euclid, he was less formal and more clearly than the other mathematicians to it (for example, Peano and Pash), to demonstrate the essence of the axiomatic method. On the basis of lectures at the University of Gottingen was written small - only 92 pages - book Foundations of geometry, mathematics became a bestseller. The book Foundations of Geometry was immediately translated into many languages. Meanwhile, Gilbert began to publish works in another, an entirely new field of mathematics.

In the summer of 1899, he turned to the famous problem known as the Dirichlet principle. In the same period, Gilbert continued to publish work in the field of geometry, wrote a concept of number.

In the summer of 1900 in Paris it was to be held the Second International Congress of Mathematicians, and Gilbert was invited to perform it with one of the keynote speeches. The report with the modest title Mathematical problems they were formulated 23 tasks, staging of which was largely determined by the development of mathematics in the 20th century. The scientist, who managed to solve one of them, or to contribute to a solution, immediately became a celebrity.

After Paris, Gilbert continued his geometrical studies, but most of the time was devoted to the analysis. A new period of his creative life, during which he greatly developed the theory of Fredholm integral equations and applied it to a number of specific problems in the theory of differential equations. Of his concept of the so-called Hilbert space (generalizing the concept of Euclidean space, the infinite-dimensional case) it was one of the foundations of modern functional analysis.

Work on the integral equations led Hilbert to the border area between mathematics and physics. Gilbert felt that it was time for a project proposed by him in Paris as the sixth problem of the 20th century - the axiomatization of physics and other sciences associated with mathematics. There was a branch of physics - the kinetic theory of gases - where physical concepts naturally lead to integral equations. It was here that he began to implement his plans. After that, the unit took up the theory of radiation, which also led to the concept of integral equations. Over the next two years, Gilbert has published a series of papers in which with the help of linear integral equations obtained the basic results of this theory, laid the foundation for their axiomatic and proved the consistency of its axioms. Then Gilbert came to the molecular theory of the structure of matter and is going to take the electron theory. His approach to these regions resembled the old interpretation of the kinetic theory, but have never been published. With great interest the Einstein Hilbert attempts to create a general theory of relativity. The two scientists came to a goal almost simultaneously: Einstein introduced the Berlin Academy his two works on the general theory of relativity, 11 and 25 November 1915, Hilbert also gave the Royal Society in Gottingen his first note Foundations of Physics 20 November. Despite these impressive results, the idea of ??Hilbert "shackle physics" in the framework of the axiomatic approach failed.

By the winter of 1920-1921 Hilbert`s interests began to shift again in the area of ??mathematics. Now, his main goal was the logical formalization of the foundations of mathematics. By 1922 he had formed an extensive plan formalization of mathematics, followed by proof of the consistency of formal mathematics. In 1934 and 1939 it came out two volumes of the foundations of mathematics, written by Gilbert, together with his assistant P.Bernaysom.

In January 1930, Gilbert turned 68 years old - the age at which a professor in Germany had to retire. In the winter semester of 1929-1930 he gave his "Farewell to the pedagogical activity", and the spring of 1930 resigned. His successor at the department became Weil.

In 1932 elections won by the National Socialist Party, and in January the following year Hitler became Chancellor of Germany. Almost immediately after these universities were ordered to fire from their state of the Jewish teachers. Hitler`s ultimatum applied to so many professors of the Mathematical Institute in Gottingen: to the Courant, Landau, E.N