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Less confusing phrasing.
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Gelfand-Mazur — every real unital Banach algebra where every non-zero element is invertible is isomorphic to either $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$ — was first published without proof by Mazur. HeMazur had a (rather short) proof, but the editor demanded he shortened it further. He refused to doshorten it, and so it was published without proof.

Later Gelfand later published a proof of a weaker version (only for complex commutative Banach algebras), probably without knowing about Mazur's result.

Gelfand-Mazur — every real unital Banach algebra where every non-zero element is invertible is isomorphic to either $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$ — was first published without proof by Mazur. He had a proof, but the editor demanded he shortened it. He refused to do it, Gelfand later published a proof of a weaker version (only for complex commutative Banach algebras), probably without knowing about Mazur's result.

Gelfand-Mazur — every real unital Banach algebra where every non-zero element is invertible is isomorphic to either $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$ — was first published without proof by Mazur. Mazur had a (rather short) proof, but the editor demanded he shortened it further. He refused to shorten it, and so it was published without proof.

Later Gelfand published a proof of a weaker version (only for complex commutative Banach algebras), probably without knowing about Mazur's result.

fix parenthetic phrase with something that looks ok.
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Mark Hurd
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Gelfand-Mazur (every— every real unital Banach algebra where every non-zero element is invertible is isomorphic to either $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, was first published without proof by Mazur. He had a proof, but the editor demanded he shortened it. He refused to do it, Gelfand later published a proof of a weaker version (only for complex commutative Banach algebras), probably without knowing about Mazur's result.

Gelfand-Mazur (every real unital Banach algebra where every non-zero element is invertible is isomorphic to either $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, was first published without proof by Mazur. He had a proof, but the editor demanded he shortened it. He refused to do it, Gelfand later published a proof of a weaker version (only for complex commutative Banach algebras), probably without knowing about Mazur's result.

Gelfand-Mazur — every real unital Banach algebra where every non-zero element is invertible is isomorphic to either $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$ was first published without proof by Mazur. He had a proof, but the editor demanded he shortened it. He refused to do it, Gelfand later published a proof of a weaker version (only for complex commutative Banach algebras), probably without knowing about Mazur's result.

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Gelfand-Mazur (every real unital Banach algebra where every non-zero element is invertible is isomorphic to either $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, was first published without proof by Mazur. He had a proof, but the editor demanded he shortened it. He refused to do it, Gelfand later published a proof of a weaker version (only for complex commutative Banach algebras), probably without knowing about Mazur's result.