He proposed an axiomatization of Euclidean geometry different from Hilbert 's ( see Birkhoff 's axioms ) ; this work culminated in his text Basic Geometry ( 1941 ) .
He also worked on number theory , the Riemann -- Hilbert problem , and the four colour problem .
He proposed an axiomatization of Euclidean geometry different from Riemann -- Hilbert 's ( see Birkhoff 's axioms ) ; this work culminated in his text Basic Geometry ( 1941 ) .
He also worked on number theory , the Riemann -- Hilbert problem , and the four colour problem .