We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.

Summary

This quote suggests that mathematical geometry should not be understood as a study of visual spatial structures meant for accommodating physical objects. Instead, it should be seen as a theoretical framework dealing with abstract mathematical spaces known as manifolds. In other words, the focus of mathematical geometry is not on visual or physical manifestations of space, but rather on the conceptual structures and relationships within these spaces.

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