Kurt Gödel and the Logic of Concepts

Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are based on remain unclear. In this article, we focus on the concept of mathematical beauty, as one of the central aesthetic concepts in mathematics. We propose an account according to which beautiful mathematics is one in which a great deal of the mathematical world is reflected. We argue that beauty in mathematics reveals connections between apparently non-related problems or areas and provides a wider insight into mathematical reality as a whole. We also analyze the close relationship between beauty and other important notions such as depth, elegance, simplicity and others.