Historians are constantly confronted with the twin problems of translating texts and interpreting their meanings. When mathematicians like Georg Cantor or Abraham Robinson demonstrate the consistency of concepts that, since the paradoxes of Zeno and Democritus, have been assumed to be paradoxical notions like infinitesimals or the actual infinite, how should the works of earlier mathematicians be regarded, who either used such concepts or believed they had proven their impossibility? Is it anachronistic to use nonstandard analysis or transfinite numbers to “rehabilitate” or explain the works of Leibniz, Euler, Cauchy, or Peirce, for example, as recent mathematicians, historians, and philosophers of mathematics have attempted? At the other extreme, chronologically, how may ideas readily accepted in the West – like incommensurable numbers, parallel lines, and similar triangles – but foreign to traditional Chinese mathematics have adversely affected the interpretations of ancient Chinese mathematical works?

Two parts of analysis to which Leonhard Euler contributed in the 1740s and 1750s are the calculus of variations and the theory of infinite series. Certain concepts from these subjects occupy a fundamental place in modern analysis, but do not appear in the work of either Euler or his contemporaries. In the case of variational calculus there is the concept of the invariance of the variational equations; in the case of infinite series there is the concept of summability. However, some modern mathematicians have suggested that early forms of these concepts are implicitly present in Euler’s writings. We examine Euler’s work in calculus of variations and infinite series and reflect on this work in relation to modern theories.