Hermann minkowski (1864- 1909) was born in Tass, Alekso, Russia (now kaunas, Lithuania). My father was a successful Jewish businessman, but the Russian government persecuted Jews at that time, so when Minkowski was eight years old, his father and his family settled in Konigsberg, Prussia, just across the river from the home of another mathematician, Hilbert. Minkowski has two brothers. Is he a younger brother? Big brother Max couldn't go to school because of racial discrimination when he was in Russia. Later, he never received formal education. When he grew up, he went into business with his father, inherited his father's mantle and became a successful businessman. The second brother is Oscar Minkowski, a famous medical scientist, who discovered the relationship between insulin and diabetes and was called "the father of insulin". Minkowski himself was called a prodigy because of his outstanding mathematical ability, and later he became an excellent mathematician. All three of them are excellent and once made a sensation in Konigsberg.

1873, Minkowski entered Elstat Preparatory School. His quick thinking and excellent memory soon showed his talent in mathematics. Not only that, Minkowski is familiar with the works of Shakespeare, Schiller and Goethe, and Goethe's Faust can almost be memorized. This is different from Hilbert. He has a slow crow. After eight years of preparatory school courses, Minkowski completed his studies in five and a half years. So Minkowski graduated a year earlier, although he was two years younger than Hilbert. At that time, German universities were free to choose any university to register. Minkowski first entered the local university, soon transferred to the University of Berlin, and returned to the University of Konigsberg after three semesters. During his college years, his teachers were Helmholtz, leonid hurwicz, Lin Deman, Kroneck, Cuomo, Weber, Wilstras and Kirchhoff. At the University of Konigsberg, Minkowski and Hilbert met again, and they shared the same interests and became lifelong friends.

1884, 25-year-old mathematician Hurwitz came to the University of Konigsberg as an associate professor, and soon established friendship with Minkowski and Hilbert, who were closely linked by their scientific hobbies. Every afternoon at five o'clock, we can see the three of them walking in the apple orchard, discussing the current math problems, sometimes bowing their heads and thinking hard, sometimes arguing, and sometimes laughing knowingly. Others seem to be really a bunch of math lunatics. However, these discussions have an important influence on their respective mathematical work. Hilbert later wrote: In countless walks, the three of us explored every corner of mathematical science. Leonid hurwicz is knowledgeable. He is always our guide. In college, Minkowski won an award for his outstanding math performance.

188 1 year, French science issued an announcement offering a reward for solving a mathematical problem: proving that any positive integer can be expressed as the sum of five squares. Minkowski, who is only ten years old, has made an achievement far beyond the original question. However, the deadline is approaching and it must be translated into French according to the rules of the game. However, Minkowski was too late, water under the bridge. He decided to give it a try The next year, the grand prize was announced. Minkowski, aged 18, and the famous British mathematician Henry Smith won the prize together. Minkowski once again caused a sensation in Konigsberg. 1In the summer of 885, Minkowski received his doctorate from the University of Konigsberg. After a short military career, he was hired as a lecturer at 1886 Bonn University. Kroneck, a professor of mathematics at the University of Berlin, died in 189 1, which caused the change of professors and associate professors in German universities. Hurwitz, an associate professor at the University of Konigsberg, was transferred to the University of Zurich as a professor of mathematics, and Hilbert took his place, while Minkowski was promoted to an associate professor at Bonn University. From 65438 to 0895, Hilbert was lured to the University of G? ttingen by Klein, and Minkowski took over his professorship at the University of Konigsberg.

1896, Minkowski transferred to Zurich University and Herwitz University. Einstein, the master of physics, is his student. 1902, Minkowski was also snared by Klein and joined the forest of mathematics masters at the University of G? ttingen until his death. Minkowski got married on 1897, and his wife, August Adler, is the daughter of a leather factory director near Konigsberg. They have two daughters. 190965438+1October 10, Minkowski suddenly had acute appendicitis at the peak of his creativity, and the rescue was ineffective. Unfortunately, he died in 65438+ 10/2 at the age of 45. Hilbert, a close friend before his death, sorted out his posthumous works and published The Complete Works of Minkowski in 19 1 year.

Minkowski's main work is number theory, algebra and mathematical physics. In number theory, he made an important research on quadratic form. In the 188 1 France Prize, Minkowski studied the works of Gauss, Dirichlet and Einstein in depth. Because Gauss used the property of binary quadratic form when studying the decomposition of an integer into three square sums, Minkowski realized from his predecessors' work that the method of decomposing an integer into five square sums was related to quaternary quadratic form. As a result, he deeply studied the quadratic form of n elements and established a complete theoretical system. In this way, the original problem can be easily drawn from a more general theory. Minkowski's paper to French Academy of Sciences is 140 pages long, which is far beyond the scope of the original question.

After that, Minkowski continued to study the theory of N-ary quadratic form. He described the equivalence of quadratic forms with rational coefficients under the linear transformation of rational coefficients through three invariants, and completed the reduction theory of positive definite quadratic forms with real coefficients (1905), which is now called Minkowski's reduction theory. Minkowski got a very wonderful and clear result when he studied the simplification of n-ary quadratic form by geometric method. He called the number theory thus established "the geometry of numbers". This leads to his research on convex geometry, and the by-product of this research is the famous Minkowski inequality: {∑ (AK+BK) r}1/r ≤ {∑ Akr}1/r+{∑ bkr}1r.

Minkowski was interested in mathematical physics in his early years. When he was working in Bonn University, he helped physicist Hertz to study electromagnetic wave theory. After 1905, he devoted almost all his energy to electrodynamics. 1907, Minkowski realized that the work of Lorenz and Einstein can be understood by the idea of non-Euclidean space. He believes that the concepts of time and space, which were always regarded as independent in the past, can be combined in a four-dimensional space-time theory: ds2 = c2dt2+dx2+dy2+dz2, which was later called "Minkowski's world". Therefore, different descriptions of the same phenomenon can be expressed in a simple mathematical way. These works provide a framework for special relativity. M. Bonn, winner of the Nobel Prize in Physics, once said that he found "the whole arsenal of relativity" in Minkowski's mathematical works. Minkowski's works in this field mainly include Laum and Time 1907 and Zwei Abuhanlong, Enuel Di Grundgretchengen de Electrodynamics 1909.