David Hilbert : 1862-1943
David Hilbert is known as one of the most important people who contributed to the development of mathematics in the modern era. He was born in 1862 near Konigwarg in eastern Persia. He was the son of the then District Judge. In 1880, he joined the local university of Königsberg University. Where Kant studied and taught. Königsberg was far from Göttingen and Berlin as centers. Hilbert completed his graduation in 1885 and started working as an assistant professor in 1892. He then also became head of mathematics at Göttingen at the request of Felix Keen. Gauss worked in Göttingen as a famous and creative mathematician in the nineteenth century. Hilbert then stayed in Göttingen, assuming the same role as Gauss and exhibiting similar abilities.
By 1898, Hilworth was working with interest on the theory of algebraic numbers. But in the winter season of 1898-1899, he presented several lectures based on the postulates of Euclidean geometry. He also published an edited book Grundlagender Geometric (Foundation for Geometry) contained in small units and of slim size. The 92-page geometry book attracted the attention of scholars from the mathematical world. A French edition was also published and an English version was also published. The German edition was published 7 times during Hilbert's lifetime. Paul Bernays published its eleventh edited edition. which was twice as large as the initial state publication. Legendre also published a book on geometry called Elements de ge'ometrie. which outsold Hilbert's book. But Hilbert's book was for students of mathematics while Legendre's book was curriculum focused.
Hilbert developed the Hilbert model of Euclidean geometry using modern axioms in the field of geometry. He used four undefined terms including point, line, plane, on (incidence of point to live). He distinguished between lines and line segments. For that he mentioned the following definition.
Line segment AB, The set of all points that are between A and B. Points A and B are called the end points of the segments.
He developed many axioms regarding the development of geometry. He divided those axioms into five groups. Among that group, the first group is mentioned in relation to Line and Point. It consists of four axioms called Axioms of connection. Similarly, the second group is named Axioms of order by including the order of points, which includes four axioms. The third group includes the axioms of conformity. which are called axioms of congruence. It contains five axioms. The fourth group consists of axioms of parallel which contains only one axiom. The fifth group includes axioms of continuity. It contains two axioms. But although he mentioned 21 axioms in five groups, nowadays 16 are more discussed.
He noted how the logical difficulty of Euclidean geometry arose by grouping the 21 axioms into five groups in this way. In this way, he worked to organize Euclid's geometry logically, which seems to have contributed significantly to the development of geometry. Among the contributions he made in the field of mathematics, his contribution in the field of geometry has been mentioned elsewhere. He has contributed in other fields besides geometry. Those contributions are summarized as follows.
• Contributed to the development of the philosophy of mathematics: Hilbert studied mathematical logic and mentioned formalism as a mathematical philosophy, which tried to solve the philosophical problems of mathematics to some extent.
• Developed the Hilbert model of Euclidean geometry based on Euclidean geometry.
• Mentioning Hilbert space and developed functional analysis in it.
• Mentioned things like Hilbert metric, Hilbert number, Polynomial Hilbert's Poincare series, Hilbert Spectrum, Hilbert symbol, Hilbert theorem on differential geometry.
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