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首页> 外文会议>Wessel Symposium on Around Caspar Wessel and the Geometric Representation of Complex Numbers, Aug 11-15, 1998, Copenhagen >Priority Claims and Mathematical Values: Disputes over Quaternions at the end of the Nineteenth Century
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Priority Claims and Mathematical Values: Disputes over Quaternions at the end of the Nineteenth Century

机译：优先权主张和数学价值：十九世纪末关于四元数的争论

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What was the effect of Tait's response? There is more than one answer. As far as quaternions proper were concerned, we see some acknowledgement of Tait's remarks in the relevant articles of the Encyklopaedie der mathematis-chen Wissenschaften. Writing in 1898, E. Study repeats the claim in Klein's paper in the first volume, before Tait's claims were made (Study 1898 p. 183). H. Rothe's article in the third volume accepts Valentiner's claim of the priority of Wessel over Argand, but further states of Gauss that he had the multiplication theorem for quaternions in 1819 or 1820 ― a more restricted claim than that of Klein; he furthermore notes Tait's article, though he does not comment on its content. By 1905, however, Study was more measured in his comments. In (Study, 1905, 423) he claims that Gauss had the multiplication theorem, but further remarks: With this, however, he was far from possessing the entire theory of Quaternions, for which among other things the association of vectors with simple figures in space ― pairs of vectors ― is essential. We must concur with English authors when they seek to treat Hamilton as the true discoverer of the quaternion theory after [the discovery of Gauss' work] as well as before. The further assertion that there is a difference of principle between Gauss' four-tuple and Hamilton's quaternions seems to us unconvincing. (Study, 1905, 423) Study thus yielded to the view of Tait that Gauss lacked the full power of the quaternion theory, while nevertheless holding out in support of Klein's view, and against Tait's, that Gauss and Hamilton were not so very different in their ways of thinking. There is another aftermath, however, one which would take us too far afield to explore in detail, but which should be mentioned. This is in the context not of quaternions but of vector calculus, where many of the most important quaternion notions eventually came to roost. Recasting quaternion notions gave further opportunities to examine their roots, For example, we find Emil Jahnke in 1905 tracing vectorial analysis to the barycentric calculus of Moebius ― again a German priority over Hamilton, this time a published one. Quaternions were eventually marginalized completely as vector calculus became the norm, pushing debates concerning their priority well into the background.
机译：Tait回应的结果是什么？答案不只一个。就适当的四元数而言，我们在《数学史》（Encyklopaedie der Mathematis-chen Wissenschaften）的相关文章中看到了泰特的言论。 E. Study于1898年撰写，在提出Tait主张之前，在第一卷中重复了Klein论文中的主张（Study 1898 p。183）。 H. Rothe在第三卷中的文章接受了Valentiner主张Wessel优先于Argand的优先权，但高斯进一步指出，他在1819或1820年有四元数的乘法定理–比Klein的主张更为严格；他还注意到Tait的文章，尽管他未评论其内容。然而，到1905年，研究在他的评论中得到了更大的衡量。在（Study，1905，423）中，他声称高斯具有乘法定理，但进一步说明：然而，他并没有掌握四元数的全部理论，为此，除其他外，向量与简单图的关联空间-向量对-是必不可少的。当英国作家试图将汉密尔顿视为四元数论的真正发现者（无论是在发现高斯的著作之后）还是之前，我们必须同意他们的观点。对于高斯的四元组和汉密尔顿的四元数之间存在原理差异的进一步断言，在我们看来并不令人信服。 （Study，1905，423）因此，研究得出了泰特的观点，即高斯缺乏四元数理论的全部力量，尽管如此，他仍然支持克莱因的观点，而反对泰特的观点是，高斯和汉密尔顿在观点上并没有太大不同他们的思维方式。然而，还有另一种后果，那就是将我们带到了一个遥远的地方，无法详细探讨，但应该提及。这不是在四元数的上下文中，而是在矢量演算的上下文中，其中许多最重要的四元数概念最终浮出水面。重铸四元数的概念提供了进一步检查其根源的机会，例如，我们发现1905年的Emil Jahnke将矢量分析追溯到Moebius的重心微积分-再次是德国人优先于汉密尔顿，这次是出版的。随着向量演算成为常态，四元数最终被完全边缘化，从而将有关其优先级的辩论很好地推向了背景。

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