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Single Idea 13472

[filed under theme 6. Mathematics / A. Nature of Mathematics / 2. Geometry ]

Full Idea

One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry.

Gist of Idea

Hilbert aimed to eliminate number from geometry

Source

report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2

Book Ref

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.42

A Reaction

Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths).

The 4 ideas from 'Foundations of Geometry'

13472 Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
9546 Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
18742 Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
18217 Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]