Hilbert's fourth problem

In mathematics, Hilbert's fourth problem in the 1900 Hilbert problems was a foundational question in geometry. In one statement derived from the original, it was to find geometries whose axioms are closest to those of Euclidean geometry if the ordering and incidence axioms are retained, the congruence axioms weakened, and the equivalent of the parallel postulate omitted. A solution was given by Georg Hamel.

The original statement of Hilbert, however, has also been judged too vague to admit a definitive answer.

References

• Busemann, Herbert (1976). "Problem IV. Desarguesian spaces". In Browder, Felix E.. Mathematical Developments Arising from Hilbert Problems. Proceedings of Symposia in Pure Mathematics. XXVIII. American Mathematical Society. pp. 131–141. ISBN 0-8218-1428-1. Zbl 0352.50010.