# Definition:Hilbert 23/4

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## Hilbert $23$: Problem $4$

### Construction of all Metrics where Lines are Geodesics

Construct all metrics where lines are geodesics.

Construction of all Metrics where Lines are Geodesics

## Historical Note

The **Hilbert 23** were delivered by David Hilbert in a famous address at Paris in $1900$.

He considered them to be the oustanding challenges to mathematicians in the future.

There was originally going to be a $24$th problem, on a criterion for simplicity and general methods in proof theory, but Hilbert decided not to include it, as it was (like numbers $4$, $6$, $16$ and $23$) too vague to ever be described as "solved".