Anachronisms in the History of Mathematics: Essays on the Historical Interpretation of Mathematical Texts , by Niccolò Guicciardini, ed.

Abstract

figures in early non-Euclidean geometry, Lobachevskii and János Bolyai. Gray examines the misunderstanding of their work by Bonola. This misunderstanding partly arises from an anachronistic view of what is elementary and what is not. He shows how this then affects how one sees the development of a mathematical subject, in particular the degree to which Riemann’s work represented a leap or step forward in the development of non-Euclidean geometry. Lorenat’s anachronism, accordingly, concerns the validity of characterizing an area of mathematics in terms of its content and presumed purpose, while Gray focuses on the mathematical methods employed and their characterization as either elementary or advanced.