Definition:Hilbert 23/9

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Hilbert $23$: Problem $9$

General Reciprocity Theorem in Algebraic Number Field

Find the most general law of the Reciprocity Theorem in any algebraic number field.

General Reciprocity Theorem in Algebraic Number Field

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".