Detlef Laugwitz

Detlef Laugwitz (1932-2000) was a mathematician and historian of mathematics. He published the standard biography of Bernhard Riemann in 1996. He authored a series of publications in professional history of mathematics journals on both Euler and Cauchy. See

Laugwitz, D. (1987). Infinitely small quantities in Cauchy's textbooks. Historia Mathematica 14, 258-274. https://doi.org/10.1016/0315-0860(87)90045-0

Laugwitz, D. (1989). Definite values of infinite sums: aspects of the foundations of infinitesimal analysis around 1820. Archive for History of Exact Sciences 39 (3): 195-245. https://link.springer.com/article/10.1007/BF00329867

Laugwitz, D. (2002). Debates about infinity in mathematics around 1890: The Cantor-Veronese controversy, its origins and its outcome. N. T. M. 10, 102-126.

Here Laugwitz wrote: "In the realm of the finite it does not really matter mathematically whether we consider the natural numbers as ordinals or as cardinals or as constituents of an algebraic structure. Cantor had succeeded in showing, by different laws holding for transfinite ordinals and cardinals, that the infinite could clarify the conceptual distinctions. To Stolz, Veronese and Levi-Civita we owe early insights in ordered mathematical structures as a third aspect of the number concept. This approach prepared the ground for twentieth century developments." (p. 103)