KLEIN VS MEHRTENS: RESTORING THE REPUTATION OF A GREAT MODERN JACQUES BAIR, PIOTR BL ASZCZYK, PETER HEINIG, MIKHAIL G. KATZ, JAN PETER SCH¨AFERMEYER, AND DAVID SHERRY 【摘要】历史学家赫伯特·梅尔滕斯(Herbert Mehrtens)试图将世纪之交的数学史描绘成一场现代与反现代的斗争，这两阵营分别由大卫·希尔伯特(David Hilbert)领导的现代和菲利克斯·克莱因(Felix Klein)领导。Mehrtens的一些结论被历史学家(杰里米•格雷饰)和数学家(弗兰克•奎因饰)采纳。 我们认为，同在哥廷根的克莱因和希尔伯特并不是对手，而是现代主义的盟友，他们的目的是拓宽数学的范围，而不是像柏林学派那样仅仅关注算术化分析。 克莱因的Gottingen讲座和其他文本阐明了克莱因的现代主义。希尔伯特对直觉的看法比梅尔滕斯愿意接受的更接近克莱恩的观点。克莱因和希尔伯特对物理学的公理化同样感兴趣。Klein的功劳包括帮助开启了亚伯拉罕•弗伦克尔(Abraham Fraenkel)的职业生涯，并推动了索菲斯•利(Sophus Lie)、埃米•诺特(Emmy Noether)和恩斯特•泽梅洛(Ernst Zermelo)的职业生涯，这四个人无疑都是无可挑剔的现代主义者。 梅尔滕斯声称希尔伯特的兴趣在生产而不是意义上，这一未经证实的说法似乎源于梅尔滕斯的马克思主义倾向。梅尔滕斯声称 “Theodor Vahlen……引用克莱因在数学上的种族主义区别，并将其激化为公开的反犹主义”，这伪造了在提到的克莱因和Theodor Vahlen这两个人物之间虚假的连续性，因此是对克莱因立场的不当误读。” 【Abstract】 Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Klein. Some of Mehrtens’ conclusions have been picked up by both historians (Jeremy Gray) and mathematicians (Frank Quinn). We argue that Klein and Hilbert, both at G¨ottingen, were not adversaries but rather modernist allies in a bid to broaden the scope of mathematics beyond a narrow focus on arithmetized analysis as practiced by the Berlin school. Klein’s G¨ottingen lecture and other texts shed light on Klein’s modernism. Hilbert’s views on intuition are closer to Klein’s views than Mehrtens is willing to allow. Klein and Hilbert were equally interested in the axiomatisation of physics. Among Klein’s credits is helping launch the career of Abraham Fraenkel, and advancing the careers of Sophus Lie, Emmy Noether, and Ernst Zermelo, all four surely of impeccable modernist credentials. Mehrtens’ unsourced claim that Hilbert was interested in production rather than meaning appears to stem from Mehrtens’ marxist leanings. Mehrtens’ claim that “Theodor Vahlen ...cited Klein’s racist distinctions within mathematics, and sharpened them into open antisemitism” fabricates a spurious continuity between the two figures mentioned and is thus an odious misrepresentation of Klein’s position. Klein vs Mehrtens: restoring the reputation of a great modern arxiv.org Matches for: MR=3819950 mathscinet.ams.org http://dx.doi.org/10.15330/ms.48.2.189-219 dx.doi.org
标签: 现代主义
