The author, a Pure Mathematician and a Structural Engineer, tries to prove that there cannot be any relationships between pure mathematics an concrete 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.
He next explains that his work with some of the greatest architects of this century has shown him that architecture is one of the most demanding activities of man and that, interested as he is about architecture, he does not dare to work as an architect, and is satisfied with only helping architects with his knowledge of structures.
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.
There are so many knowledgeable architects and theoreticians of architecture at this meeting that he does not dare to complete with them, and brings his presentation to a close.