Hilbert Foundations of Geometry
Grundlagen der Geometrie: axiomática formal moderna
- Date
- 1899 · confidence high
- Place
- Göttingen, Germany
- Credited to
- David Hilbert
- People
- 👤 David Hilbert1862–1943
- Field
- Knowledge & symbols
What was discovered
A complete re-axiomatisation of Euclidean geometry with 20 axioms, an analysis of their independence and consistency, and the idea that primitive terms carry no meaning (tables, chairs and beer mugs). It fixes the modern ideal of a formal system.
He reduced the consistency of geometry to that of arithmetic, which motivated Hilbert's second problem.
What it led to
- Hilbert's programme
- metamathematics
- model theory
- Bourbaki structuralism
Built on
- Euclidean axiomatic geometryc. 300 BCE
- Pasch (1882)
- non-Euclidean geometries