After Hilbert, he took over the overall situation - Hermann Weyl
—Read the summary of the Golden Age of the Göttingen School (1918-1933) in 20th Century Mathematics (20th Century) 6
Hilbert is getting old, and his heir is in his prime, following in his historical footsteps and ushering in the brilliant life of a mathematical master, he is Hermann Weyl.
Hermann Weyl (1885-1955), born in Elmshorn near Hamburg, Germany, received his doctorate from the University of Göttingen in 1908 and was director of the Göttingen Institute of Mathematics and professor at the Institute for Advanced Study in Princeton. He was one of the most important mathematicians of the first half of the 20th century, made significant contributions to many fields of mathematics, and made outstanding achievements in the theory of relativity and quantum mechanics.
Weyl was born in a small town in Hamburg to a banker father and a housewife mother. The countryside was more closed, but Weyl showed great talent in mathematics and science early on. He dabbled in a wide range of disciplines and had read Kant's Critique of Pure Reason in secondary school.
Fortunately, the headmaster of the school was Hilbert's cousin, who specially introduced him to the mathematics department of the University of Göttingen, where Hilbert was located, and became Hilbert's heir in the future...
In 1913, he not only married, but was also hired as a professor at the Swiss Technical University in Zurich, and met Einstein, who worked with him, and was impressed by Einstein's new ideas in physics.
The decade after World War I was Weyl's golden decade of mathematics, and Germany twice invited him to return to the University of Göttingen, replacing the retired Klein and the elderly Hilbert. The sad alma mater, the mentor who missed him, finally accepted the invitation. But for a long time, due to the rise of German fascism and political turmoil, he had to listen to the advice of Einstein, who arrived in the United States early, and came to the Princeton Research Institute in 1933 to spend the second half of his life.
Weyle, who has passed the golden age of mathematics, attracted a large number of mathematicians to Princeton, and his profound knowledge and wisdom guided the direction of young students. Princeton became the center of mathematics in the world, replacing Göttingen.
Weyl's role was significant, and countless young people missed his help, including Chen Province in China, who wrote...
Weyl 's achievements were both mathematical and physical , and his major works : " Space , Time , Matter " , " Riemann Surfaces " , " Group Theory and Quantum Mechanics " , " Canonical Groups " , and " Symmetry " . In the eyes of mathematicians, he is a master of mathematics; In the eyes of physicists, he was a pioneer of quantum theory and relativity; He is also the inventor of gauge field theory, the most important theory of particle physics today. ......
Mathematically following Hilbert's study of Riemannian surfaces after integrating differential equations, became the source of complex manifolds, algebraic topology, algebraic geometry...
Physics invested in general relativity, trying to link philosophy, mathematical methods, and physical theories, and in 1918 he proposed the normative theory, and later Yang Zhenning was inspired to generalize from electromagnetism, with Yang Zhenning-Mills non-commutative gauge field theory...
He always combines the latest mathematics with physics. When quantum mechanics was first produced, in 1927 Weyl published "Group Theory and Quantum Mechanics", which became an essential book for later theoretical physicists, too abstract to read through many people...
Many years after Weyl's death, his presence is still felt everywhere in the mathematical and physics circles, and his profound mathematical ideas are like guiding lights, and his work affects the twenty-first century.
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