戴森讲述数学与物理往事(cast. 冯诺伊曼, 希尔伯特, 海森堡, 狄拉克etc.

摘自戴森(Freeman Dyson)为冯诺伊曼(John von Neumann)的著作<Mathematical Foundations Of Quantum Mechanics>写的序——“

During his Berlin years, Johnny made frequent visits to Göttingen, where Heisenberg had recently invented quantum mechanics and Hilbert was the presiding mathematician. Hilbert was intensely interested in quantum mechanics and encouraged collaboration between mathematicians and physicists. From the point of view of Hilbert, quantum mechanics was a mess. Heisenberg had no use for rigorous mathematics and no wish to learn it. Dirac made free use of his famous delta-function, which was defined by a mathematical absurdity, being infinite at a single point and zero everywhere else. When Hilbert remarked to Dirac that the delta-function could lead to mathematical contradictions, Dirac replied, “Did I get into mathematical contradictions?” Dirac knew that his delta-function was a good tool for calculating quantum processes, and that was all that he needed. Twenty years later, Laurent Schwartz provided a rigorous basis for the delta-function and proved that Dirac was right. Meanwhile, Johnny worked with Hilbert and published a series of papers cleaning up the mess. In 1932 he published the book Mathematical Foundations of Quantum Mechanics, which occupies a substantial piece of his garden.

...The culture of physics was dominated by people like Oppenheimer who made friends with poets and art historians but not with pure mathematicians. The culture of mathematics was dominated by the Borbaki cabal, which tried to expunge from mathematics everything that was not purely abstract. The gap between physics and mathematics was as wide as the gap between science and the humanities described by C. P. Snow in his famous lecture on the two cultures. Johnny was one of the very few people who were at home in all four cultures: in physics and mathematics, but also in science and the humanities.

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