In this paper I discuss the importance of research in the history of Mathematics for the training of mathematics teachers and argue that it is possible to see historical research in a pedagogical light as a creativity exercise which provokes the mathematical creative process, in mathematics' classes. I mention examples of mathematicians who gathered a set of cognitive skills to reinvent mathematical principles in the explanation of challenging themes in mathematics. It is about seeking in the history of mathematical practices and elaborations, in its experimental and formal levels, aspects that define the outline of the challenges which lead to the production of mathematical knowledge currently addressed in Middle, High and Upper Education. I present two historical examples in order to show how the creative spirit is of fundamental importance in the mathematical training of students of basic education as well as that of the mathematical teacher.
