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While the Kronecker-Weber theorem —that every finite abelian extension of $\mathbb Q$ is contained in a cyclotomic field— is always attributed to, well, Leopold Kronecker and Heinrich Martin Weber, most sources I've seen tyhat that care to go into such details observe that their proofs were incomplete and were later fixed by others, among which one usually finds Hilbert named (One extreme example: Wikipedia even states that Kronecker conjectured the result!)

When was the theorem finally proved, exactly?

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While the Kronecker-Weber theorem —that every finite abelian extension of $\mathbb Q$ is contained in a cyclotomic field— is attributed to, well, Leopold Kronecker and Heinrich Martin Weber, most sources I've seen tyhat care to go into such details observe that their proofs were incomplete and were later fixed by others, among which one usually finds Hilbert named (One extreme example: Wikipedia even states that Kronecker conjectured the result!)

When was the theorem finally proved, exactly?

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# The first complete proof of the Kronecker-Weber theorem

While the Kronecker-Weber theorem —that every finite abelian extension of $\mathbb Q$ is contained in a cyclotomic field— is attributed to, well, Leopold Kronecker and Heinrich Martin Weber, most sources I've seen care to go into details observe that their proofs were incomplete and were later fixed by others, among which one usually finds Hilbert named (One extreme example: Wikipedia even states that Kronecker conjectured the result!)

When was the theorem finally proved, exactly?