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. Moreover, Bueno offers a criterion that establishes a minimal unity of structure to a notion of style, even in mathematics. 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.