# Definition:Hilbert 23/12

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## Contents

## Hilbert $23$: Problem $12$

### Extension of Kronecker-Weber Theorem to any base Number Field

Extend the Kronecker-Weber Theorem on abelian extensions of the rational numbers to any base number field.

Extension of Kronecker-Weber Theorem to any base 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".

## 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")