On Forming the Concept of Space – Mathematics Is Clairvoyance!

The lecture describes mathematics as a form of “clairvoyance” in which the human being actively forms supersensible ideas out of inner activity. Numbers and geometric forms are not objects perceptible to the senses but spiritual shapes that arise through will, the sense of movement and the power of imagination. Drawing on developmental psychology, embryology, pedagogy and biographical experience, it shows how mathematical thinking emerges from inner form-giving. Geometry serves as a model for supersensible knowledge, since it trains sense-free thinking. Mathematising appears as a creative process between dream-like thinking and conscious will and is understood as the basis for an expanded, renewed science.

A contribution by Detlef Hardorp to the mathematical study conference in October 2025 at the Goetheanum.

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Publication: 10 April 2026