``The last aim is always the representation of a function'': foundation of analysis in Weierstrass in 1886, historical roots and parallels (Q1206482)

\textit{R. Siegmund-Schultze} did publish in 1988 the text of a course given by \textit{K. Weierstrass} in 1886 [Ausgewählte Kapitel aus der Funktionenlehre. Teubner, Leipzig (1988; Zbl 0679.01010)] on the development of the foundations of analysis from a historical perspective. The author notes that it is clear from these lectures that Weierstrass took Euler's position (a function is given by an arithmetic process) against John Bernoulli (a function is a law defined on an interval, notion taken up by Dirichlet) and was unaware of the work of the French school around 1820 both in the foundational methods of Cauchy and his work (Delta-functions) in mathematical physics. He makes the worthwhile point that the early papers have to be read in the language of their time and be translated into modern language; in this perspective, most of Cauchy's reputed errors turn out to be sound theorems that just mean something different from the apparent meaning in modern language.