Ästhetische Erfahrung Mathematik : über das Phänomen schöner Beweise und den Mathematiker als Künstler

Using attributes like beautiful, ugly or elegant to characterise proofs and theorems as well as treating mathematics as an art is common in mathematical practice but usually not studied systematically in the philosophy of mathematics. Therefore, from a philosophical point of view there are two main questions to be discussed within the aesthetics of mathematics: 1. Which concept of beauty is used? 2. Can mathematics to some extent be considered as art?
By analysing statements of active mathematicians and philosophical literature on mathematical practice, four complexes of aesthetic properties can be identified. By means of historical case studies and in opposition to the critical position of Immanuel Kant, mathematical beauty can be characterised as a subjective pleasure based on intellectual and emotional experiences.
Treating mathematics as a kind of art establishes a special perspective on the mathematical objects and the involved people as well as on the history of mathematics. This again can be seen in contrast to the position of Kant – especially against the mathematical genius. The analysis shows similarities of mathematics and the fine arts in many respects and that the aesthetical perspective provides an appropriate characterisation of mathematical practice.
By taking an aesthetical point of view on questions concerning the teaching and learning of mathematics and by illustrating the results on classics of the aesthetics of mathematics the theoretical results are concretised. Furthermore this underlines the relevance of aesthetical experiences within mathematics.