Definition:Hilbert 23/20

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Hilbert $23$: Problem $20$

Existence of Solutions of Variational Problems with certain Boundary Conditions

Do all variational problems with certain boundary conditions have solutions?

Existence of Solutions of Variational Problems with certain Boundary Conditions

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".