常规争议：梅森书信中的数学挑战
Routine Controversies : Mathematical Challenges in Mersenne's Correspondence
摘要：
数学挑战是早期现代数学史上的一大亮点。虽然文化历史学家试图将这些挑战置于当代实践的背景下，特别是竞争市场中的决斗或广告，从而强调其人际和社会层面，但数学历史学家通常将其视为前科学时代的幼稚残余，现代科学的到来及其培根式的有效合作理想将很快结束。然而，挑战的数量并没有减少，而是在第一个旨在合作工作的科学组织之一-Marin Mersenne的网络中成倍增加。这一悖论暗示了本文的重点：审视挑战在近代法国早期数学交流（和数学创造）经济中的作用。通过成功的例子，以及不成功的挑战，我们将看到挑战是如何运作的，不仅是作为方法论对立的“mises en scène”，而且主要是作为围绕问题解决的对应关系内部结构化的数学环境中的链接。这种情况也说明了争议如何可能是正常科学活动的一个组成部分-而不是它们的破坏-同时在特定的，有限的方向上塑造它们的发展。
英文摘要：
Mathematical challenges punctuate the history of early modern mathematics. While cultural historians have attempted to contextualize these challenges among contemporary practices, in particular duels or advertisements in a competitive market, thus emphasizing their interpersonal and social dimensions, historians of mathematics have generally treated them as somewhat childish remnants of a pre-scientific age, that the advent of modern science and its Baconian ideal of efficient collaboration would soon bring to an end. However, the number of challenges did not decrease but rather multiplied inside one of the first scientific organizations aiming at cooperative work--Marin Mersenne's network. This paradox has suggested the focus of this article : to examine the role of challenges in the economy of mathematical exchange (and mathematical creation) in early modern France. Through examples of successful, but also of unsuccessful challenges, we shall see how challenges operated, not only as "mises en scène" of methodological oppositions, but also, and primarily, as links in a mathematical environment structured inside correspondences around the resolution of problems. This situation also exemplifies how controversies may have been a constitutive part of normal scientific activities--and not their disruption--while shaping their development in specific, limited directions.
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