Can There Be Any Relationships Between Mathematics and Architecture?

Abstract

The author, a pure mathematician and a structural engineer, tries to prove that there cannot be any relationships between pure mathematics and architecture, by first mentioning the variety of mathematics invented by man over the centuries. He defines pure mathematics, illustrating it by examples from Euclidean geometry and non-Euclidean geometries and pointing out the essential reality of the most abstract mathematics, including the essential importance of Riemannian geometry to the Einsteinian general theory of relativity. He then considers the essential quality of concreteness of all architecture and of its many facts, pointing out that the only real architecture must be built architecture and that no theoretician of architecture is an architect. Finally, he takes off his ‘mathematician hat’ and put on his ‘structural engineering hat’ and suddenly realizes that, yes, applied mathematics is so important to architecture that, if mathematics had not been invented, architects would have been compelled to invent it themselves.

Mario Salvadori (1907–1997).

First published as: Mario Salvadori , “Can There Be Any Relationships Between Mathematics and Architecture?”, pp. 9–13 in Nexus I: Architecture and Mathematics, ed. Kim Williams, Fucecchio (Florence): Edizioni dell’Erba, 1996.

Editors’ note: The text that follows is a transcript of the keynote address at Nexus’96: Relationships Between Architecture and Mathematics, the inaugural conference of what would become the Nexus series.