摘要：The following article aims to present the problem of the nature simple ideas for the development of science. From the perspective of Gaston Bachelard, we present two cases of geometry and physics to the problem of the simplicity of its basic concepts, from the difficulties caused by simplification to overcoming held by the deployment of simple ideas of "parallel" and “simultaneity” through the deployment of these notions. Contemporary science to use as a methodological tool to mathematical theorizing, discovers that the phenomena studied by it are composed of different types of relationships that are beyond the purely empirical analysis. Mathematics can examine more deeply the phenomenon, and discovers that what seems simple to the senses, is actually complex, because it is composed of a variety of elements. Modern scientific thought based on Cartesian always looking for the analysis of what is considered simple, and thus end up mutilating some characteristics that make up the phenomena. The mathematical method allows the deformation of simple ideas, allowing the contemporary science when necessary change its basic concepts. Advances in the area of physics and geometry are examples of reformulation of thought, due to the change of simple principles on which they were affirmed.
