This article describes the epistemology of mathematical scholarship, the constructivism view of mathematics and how mathematical learning can achieve the goals of which one is by studying discovery with a philosophical approach that emphasizes its implications on the learning of mathematics. The world of educational research, especially mathematics has shown a shift, which is more emphasize the teaching and learning process and research methods that apply the concept that, in learning someone to construct his knowledge. Humans construct their knowledge through interaction with objects, phenomena, experiences, and the environment. A knowledge is assumed to be true if it can be useful to confront and solve appropriate problems or phenomena. On constructivism view, knowledge can not be transferred from one person to another, but must be interpreted by one person individually. Knowledge is not something that is finished, but a process that develops continuously. In the process that the activity of someone who wants to know, very instrumental in the development of knowledge. Some factors such as limited previous construction experience, and a person's cognitive structure may limit the establishment of the person's personality. Conversely, conflict situations or anomalies that make people forced to think more deeply and situations that require people to defend themselves and explain in more detail, will develop one's knowledge. Constructivism is divided into three levels: radical, hypothetical realism, and the usual. This difference is based on the relationship between knowledge and existing reality.