Steiner believed in the possibility of applying the clarity of scientific thinking to spiritual experience, which he saw as deriving from an objectively existing spiritual world. Steiner identified mathematics, which attains certainty through thinking itself, thus through inner experience rather than empirical observation, as the basis of his epistemology of spiritual experience.

Section for Mathematics and Astronomy

The Mathematical-Astronomical Section is one of eleven sections of the School of Spiritual Science, Goetheanum. Its task includes research and teaching in the field of Mathematics und Astronomy in the sense of the Anthroposophical Spiritual Science as well as the coordination of the collaboration on a local, European and worldwide level.

Current research projects

The Invertible Cube

Paul Schatz discovered in 1929 that the Platonic solids could be inverted. In particular the Invertible Cube, elaborated in accordance with the respective laws, and its specific, rhythmic mobility were to become the basis upon which Paul Schatz was to build his later work. A third basic movement, a rhythmically pulsing inversion, was found and added to the two traditional basic movements of rotation (rotary motion) and translation (translational motion in a straight line). It soon became obvious that this new type of motion enabled countless and novel technical designs and approaches. More on the website of the Paul Schatz Foundation

Projective geometry

Projective geometry is not only a wonderful way of grappling with the idea of infinity in a highly satisfying manner, not only because of its didactic value to transcend the idea of metric space: The properties of dual space allow us to grapple with the notion of non-central forces. More on Projective Geometry, by Nick Thomas


Mathematics - Interview with Arthur Zajonc, Professor of Physics at Amherst College

This material was filmed in the making of Jonathan Stedall's film 'The Challenge of Rudolf Steiner'.DVD and download of the film available at