Abstract

The invention of “artificial perspective” revealed the ideal character of Euclidean geometry already in the Renaissance Europe of the fifteenth century. To the extent to which it made painting a “science” relying on mathematical rules, it made mathematics an “art” independent of the “geometry of nature.” It was the artistic vision emerging from perspective drawing that paved the way for scientific abstraction. However, it was only in the nineteenth century that the discovery of non-Euclidean geometry compelled mathematics to ponder the visual evidence of its principles and the reliability of its abstract concepts. At that time, it was the mathematical vision that first championed the rights of ideal forms to a higher level of abstraction and, therefore, oriented science and art towards new representational spaces.