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1961年在《荷兰科学院报告》上刊登了A·罗宾逊的“非标准分析”论文。论文中不仅概述了非标准分析的基本原理,而且还述及到它的某些(例如在解析力学上的)应用。在这篇论文中作者还特别强调说:“我们的首要目的就是要显示这个模型对于包含着无穷小和无穷大计算结构之经典问题所给出的另外一个自然而然的过程。大家都知道,被莱伯尼兹所坚决捍卫、被欧拉毫不动摇地采纳、而又被柯西认为其方法是合情合理的无穷小原理构成了数学分析的坚实基础。”(不过我们要指出,前文中所谓基础的坚实性应当还解决工具的复杂性和与物理直观的一致性。)
1961 in the “Netherlands Academy of Sciences” published A. Robinson's “non-standard analysis” thesis. The paper not only outlines the basic principles of non-standard analysis, but also some of its applications (such as analytical mechanics). In this dissertation, the author emphasizes: “Our primary purpose is to show another natural process of this model for the classical problems that contain infinitesimal and infinitive computing structures. As we all know, The infinitesimal principles that are resolutely defended and firmly adopted by Euler and considered by Cauchy to be justified are the solid foundations of mathematical analysis. ”(However, we should point out that the so-called solidity of the foundation should It also addresses the complexity of the tool and its intuitive physical consistency.)