159 years ago, on January 23, 1862, D. Hilbert was born
Hilbert (D. Hilbert) Hilbert，1862． 1． 23-l943. 2． 14) was a German mathematician. Born in Königsberg (present-day Kaliningrad) in East Prussia. His grandfather and father were both judges, and his mother was well educated and interested in philosophy, astronomy, and mathematics. Königsberg has a good cultural tradition, and the famous philosopher and astronomer I. Kant Kant) has worked here for life. Kant's scientific prestige and philosophical ideas had a profound influence on Hilbert from an early age. In honor of Kant, the Königsbergs erected a bust of him near Königsberg Cathedral on Kneiffanfo Island. Every October 22, on Kant's birthday, the Underground Sanctuary was open to the public: with this opportunity, like other parents, Little Hilbert's mother always liked to take her children to Kant's cemetery to admire Kant's statue. He listened carefully to his mother's account of Kant's scientific achievements and ironclad deeds, especially fond of Kant's famous words: "The most wonderful thing in the world is the brilliant starry sky above my head and the moral code of my heart." Kant's rigorous academic spirit and great reputation made Hilbert feel inspired by his love of science from an early age.
As a child, Hilbert did not show any special mathematical genius. At the age of 8 he attended the Junior Department of the Royal Frederick Preparatory School. Although the school has a long history and a very good reputation in Königsberg, the curriculum is relatively conservative, and the primary department is mainly based on language and literature, mainly reading and writing Germanic and Roba, analyzing simple sentences and some biblical stories, and having little mathematical knowledge. In the final year of the preparatory school, Hilbert transferred to the William School. The school placed a strong emphasis on mathematics and natural sciences, and even discussed certain new advances in geometry. Hilbert liked the school very much, especially studying mathematics diligently, and his grades improved rapidly. At the end of the graduation certificate, he commented: "He showed a strong interest in mathematics, and he had a deep understanding, he mastered the content taught by the teacher in a very good way, and was able to apply it with confidence and flexibility."
After graduating from preparatory school, his father insisted that he study law, but he enrolled in mathematics despite his father's objections. Dedicating his life to mathematics has become his goal. In the autumn of 1880, at the age of 18, Hilbert was admitted to the Philosophy Department of the University of Königsberg, where mathematics was based. During college, he devoted all his energy to mathematics. The famous mathematician H. Weber Weber) was his teacher, who had a great influence on him, and he studied number theory, function theory, and participated in seminars on invariants theory organized by Weber. In the next 10 years, invariant theory has been his main goal. Hilbert's doctoral dissertation was written by the famous mathematician F. Hilbert. Lindemann) was completed under the direction of. At first, he wanted to study a generalization of company scores, and Lindemann warned him that Jacobi had already done the job. At Lindemann's suggestion, Hilbert chose the problem in invariants: about the invariant properties of certain algebraic forms. The paper was brilliantly written and highly praised by Lindemann. On February 7, 1885, Hilbert was formally awarded a doctorate in philosophy by way of reply. He stayed on to teach with excellent academic results, and his academic status continued to rise in the future. He was qualified as a lecturer in July 1886, promoted to associate professor in October 1892, and professor in 1893. In 1895, the famous mathematician C. Klein (C. Klein) was introduced. F． K1ein) recommended Hilbert to become a professor at the University of Göttingen, thus beginning his golden age of scientific research.
Thanks to Hilbert's activities, the University of Göttingen became one of the world's leading mathematical research centers in the 1930s. He founded a school that had a great influence on the development of modern mathematics. In 1913 Hilbert was elected a Corresponding Member of the Berlin Academy of Sciences and in 1928 a Fellow of the Royal Society. Hilbert earned a great reputation during his lifetime. After his death, his scientific achievements and scientific spirit still influenced a new generation of mathematicians. His student, the famous American mathematician R. Curran CoLIrant, reviewing Hilbert's life's work in 1969, noted: "David Hilbert was one of the truly great mathematicians of his time. His work and the touching character of his scientific career have profoundly influenced the development of mathematical science and still do today. As a mathematical thinker, he had a deep eye, energetic, and original talent; he was versatile and had a wide range of interests; all of this made him a pioneer in many fields of mathematics. Indeed he was a man of distinction: deeply immersed in his work, dedicated to his science. He is also the best teacher and leader: open-minded and open-minded, tireless, and has a momentum that will never give up until the goal is achieved. ”
Hilbert's scientific achievements involve invariants theory, algebraic number theory, mathematical analysis, integral equation theory, geometric foundations, mathematical foundations and other mathematical fields. Opening the map of modern mathematics, you can see almost everywhere the concepts, terms, theorems, and formulas named after him: Hilbert curves, Hilbert cubes, Hilbert spaces, real Hilbert spaces, complex Hilbert spaces, quasi-Hilbert spaces, colesher Hilbert spaces, Hilbert waiting inequalities, Hilbert transforms, Hilbert polynomials, Hilbert subgroups, Hilbert modular groups. Hilbert modulo forms, Hilbert pending functions, Hilbert generalizations, Hilbert holding invariant integrals, Hilbert feature functions, Hilbert norm remaining symbols, Hilbert conjunction theorem, Hilbert's holding basis theorem, Hilbert's zero point theorem, Hilbert's irreducibility theorem, Hilbert's axiom, Hilbert's program, etc.
All of Hilbert's writings were collected and collated in The Complete Works of Hilbert (3 volumes, 1932-1935). His representative works include: On the Theory of the Relative Abelian Domain (1898), The Geometric Foundations (1899), On Logic and Arithmetic (1904), Principles of the General Theory of Linear Integral Equations (1912), Notes on the Foundations of Physics (1915), Axiomatic Thought (1917), New Foundations of Mathematics: Part I (1922), On infinity (1925), Foundations of Mathematics (1927), Fundamental Problems of Mathematics (1928), Compendium of Theoretical Logic (co-authored with Ackermann, 1928), Fundamentals of Elementary Number Theory (1930), Logic and The Understanding of Nature (1930), Proof of the Law of Exclusion (1931), Foundations of Mathematics 1 (co-authored with Berners, 1934), Foundations of Mathematics 2 (co-authored with Berners, 1939), etc. In addition, his "Report on Number Theory" at the German Mathematical Society in 1897 and his report "Mathematical Problems" at the International Congress of Mathematicians in Paris in 1990 are also precious historical documents with important academic value.