Stylistic Approach to the Brachistochrone Problem

Abstract

The notion of style is frequently used, and in some instances, without the necessary rigor. Authors such as Crombie, Hacking, Bueno and Granger consider presenting a general concept to be essential and sufficient to grasp the notion of style. They found a possibility to apply a strict concept of style even to science and mathematics. Here, using a fundamental criterion raised by Bueno (2012), I test the possibility to characterize a mathematical local style from a particular event in the history of mathematics: the Brachistochrone problem. Because this problem has different solutions, which allows them to be analyzed to verify an occurrence of style on their mathematical development. There are two problems that any concept of style should face: (i) the impregnation problem posed by Bueno and (ii) the cognitive relevance proposed by Mancosu. The former presents a serious implication in supporting a proper style in mathematics because any mathematical object needs a preceding mathematical theory that characterizes it, and if it is not possible to constitute a style in mathematics, then recognizing its cognitive relevance could also be compromised.