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Full Idea
Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms.
Gist of Idea
Hilbert's geometry is interesting because it captures Euclid without using real numbers
Source
report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3
Book Ref
Field,Hartry: 'Science without Number' [Blackwell 1980], p.25
A Reaction
Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field.