Definition:Hilbert 23/21
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Hilbert $23$: Problem $21$
Existence of Linear Differential Equation with prescribed Monodromic Group
Proof of the existence of linear differential equations having a prescribed monodromic group.
Existence of Linear Differential Equation with prescribed Monodromic Group
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".
Sources
- 1902: David Hilbert: Mathematical Problems (Bull. Amer. Math. Soc. Vol. 8, no. 10: pp. 437 – 479)
- (translated by Mary Winston Newson from "Mathematische Probleme")