The theorem can be strengthened to the claim that there are (up to isomorphism) exactly three real Banach division algebras: the field of reals R, the field of complex numbers C, and the division algebra of quaternions H.  This result was proved first by Stanisław Mazur alone, but it was published in France without a proof, when the author refused the editor's request to shorten his proof.
The theorem can be enhanced to assert that there are (up to isomorphism) exactly three real Banach division algebras: the set of real numbers R, the set of complex numbers C, and the set of quaternions H.  This finding was initially demonstrated by Stanisław Mazur in his own research, but it was published in France without a proof, as the author declined the editor's request to condense his argument.