more from David Hilbert

Single Idea 18217

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry]

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


report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3

Book Reference

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.