数学史是由胜利者书写的吗？
Is mathematical history written by the victors?
摘要：
本文从现代无穷小理论出发，考察了哲学史上关于无穷小数学起源的流行观点，并以新的视角展示了费马、莱布尼茨、欧拉、柯西等无穷小数学巨人的著作。我们还详细介绍了几个程序的历史微积分，只是澄清和形式化的现代无穷小的出现。这些程序包括费马的adequality;莱布尼茨的法律连续性和超越法律的齐性;欧拉的原则取消和无限整数与相关的无穷乘积;柯西的无穷小为基础的定义连续性和“狄拉克”δ函数。这些程序在罗宾逊的框架中被解释和形式化，如微连续性（S-连续性），标准部分原则，转移原则和超有限产品。我们评估的批评历史和现代无穷小的敌人从伯克利和康托主教和康纳斯。我们分析了历史无穷小的一致性问题，与严格性问题不同，并在这方面对比了莱布尼茨和尼翁蒂的方法。
英文摘要：
We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leibniz, Euler, Cauchy and other giants of infinitesimal mathematics in a new light. We also detail several procedures of the historical infinitesimal calculus that were only clarified and formalized with the advent of modern infinitesimals. These procedures include Fermat's adequality; Leibniz's law of continuity and the transcendental law of homogeneity; Euler's principle of cancellation and infinite integers with the associated infinite products; Cauchy's infinitesimal-based definition of continuity and "Dirac" delta function. Such procedures were interpreted and formalized in Robinson's framework in terms of concepts like microcontinuity (S-continuity), the standard part principle, the transfer principle, and hyperfinite products. We evaluate the critiques of historical and modern infinitesimals by their foes from Berkeley and Cantor to Bishop and Connes. We analyze the issue of the consistency, as distinct from the issue of the rigor, of historical infinitesimals, and contrast the methodologies of Leibniz and Nieuwentijt in this connection.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
