Full Idea
With the invention of analytic geometry (by Fermat and then Descartes) physical space could be represented as having a mathematical structure, which could eventually lead to its axiomatization (by Hilbert).
Gist of Idea
Analytic geometry gave space a mathematical structure, which could then have axioms
Source
Charles Chihara (A Structural Account of Mathematics [2004], 02.3)
Book Reference
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.43
A Reaction
The idea that space might have axioms seems to be pythagoreanism run riot. I wonder if there is some flaw at the heart of Einstein's General Theory because of this?