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One example of a missed opportunity, in my opinion, is the Aleksandrov-Zeeman theorem, which states (in one of its different forms) that any bijection of $d$-dimensional Minkowski space-time onto itself ($d>2$) which sends light ray segments into light ray segments (= Einstein's postulate of constancy of the spped of light in Special Relativity) is the composite of one or more of the following:

• A space-time translation;
• A spatial rotation;
• A scale transformation;
• A time reflection;
• A space reflection;
• And a Lorentz boost.

Particularly, this singles out Lorentz boosts as the only transformation law between inertial space-time frames obeying Einstein's postulate. Einstein did show that Lorentz boosts satisfy the latter, but he did not prove whether Lorentz boosts are unique in the above sense, neither did any of his predecessors (Lorentz, Poincaré). Surprisingly, the answer came only about half a century later, through the work of A.D. Aleksandrov in the 50's (assuming the bijection acts linearly) and independently by E.C. Zeeman in 1964 (Causality Implies the Lorentz Group, J. Math. Phys. 5 (1964) 490-493). Aleksandrov dropped the hypothesis of linearity from his argument in 1967 (A Contribution to Chronogeometry, Canad. J. Math. 19 (1967) 1119-1128).

Aleksandrov's proof was topological, based on the concept nowadays called "Alexandrov topology", which is just the order topology derived from the chronology relation in Minkowski space-time. Zeeman's proof, however, was fairly elementary and classical, relying only on bits of analytic geometry. Both the theorem and Zeeman's proof were perfectly within the grasp of the likes of Felix Klein at the time Einstein's work was published, and perfectly within the spirit of Klein's Erlanger Programm as he noticed himself by dismissing special relativity as a simple special case of his programme and calling it the "invariant theory of the Lorentz group" in his address Über die geometrischen Grundlagen der Lorentzgruppe (Jahresbericht der Deutschen Mathematiker-Vereinigung Bd. 19 (1910), pages 533-552 of his collected works). This indicates that he could have proven Zeeman's theorem at least as early as 1910, if only he had the interest.

One example of a missed opportunity, in my opinion, is the Aleksandrov-Zeeman theorem, which states (in one of its different forms) that any bijection of $d$-dimensional Minkowski space-time onto itself ($d>2$) which sends light ray segments into light ray segments (= Einstein's postulate of constancy of the speed of light in Special Relativity) is the composite of one or more of the following:

• A space-time translation;
• A spatial rotation;
• A scale transformation;
• A time reflection;
• A space reflection;
• And a Lorentz boost.

Particularly, this singles out Lorentz boosts as the only transformation law between inertial space-time frames obeying Einstein's postulate. Einstein did show that Lorentz boosts satisfy the latter, but he did not prove whether Lorentz boosts are unique in the above sense, neither did any of his predecessors (Lorentz, Poincaré). Surprisingly, the answer came only about half a century later, through the work of A.D. Aleksandrov in the 50's (assuming the bijection acts linearly) and independently by E.C. Zeeman in 1964 (Causality Implies the Lorentz Group, J. Math. Phys. 5 (1964) 490-493). Aleksandrov dropped the hypothesis of linearity from his argument in 1967 (A Contribution to Chronogeometry, Canad. J. Math. 19 (1967) 1119-1128).

Aleksandrov's proof was topological, based on the concept nowadays called "Alexandrov topology", which is just the order topology derived from the chronology relation in Minkowski space-time. Zeeman's proof, however, was fairly elementary and classical, relying only on bits of analytic geometry. Both the theorem and Zeeman's proof were perfectly within the grasp of the likes of Felix Klein at the time Einstein's work was published, and perfectly within the spirit of Klein's Erlanger Programm as he noticed himself by dismissing special relativity as a simple special case of his programme and calling it the "invariant theory of the Lorentz group" in his address Über die geometrischen Grundlagen der Lorentzgruppe (Jahresbericht der Deutschen Mathematiker-Vereinigung Bd. 19 (1910), pages 533-552 of his collected works). This indicates that he could have proven Zeeman's theorem at least as early as 1910, if only he had the interest.

One example of a missed opportunity, in my opinion, is the Aleksandrov-Zeeman theorem, which states (in one of its different forms) that any bijection of $d$-dimensional Minkowski space-time onto itself ($d>2$) which sends light ray segments into light ray segments (= Einstein's postulate of constancy of the spped of light in Special Relativity) is the composite of one or more of the following:

• A space-time translation;
• A spatial rotation;
• A scale transformation;
• A time reflection;
• A space reflection;
• And a Lorentz boost.

Particularly, this singles out Lorentz boosts as the only transformation law between inertial space-time frames obeying Einstein's postulate. Einstein did show that Lorentz boosts satisfy the latter, but he did not prove whether Lorentz boosts are unique in the above sense, neither did any of his predecessors (Lorentz, Poincaré). Surprisingly, the answer came only about half a century later, through the work of A.D. Aleksandrov in the 50's (assuming the bijection acts linearly) and independently by E.C. Zeeman in 1964 (Causality Implies the Lorentz Group, J. Math. Phys. 5 (1964) 490-493). Aleksandrov dropped the hypothesis of linearity from his argument in 1967 (A Contribution to Chronogeometry, Canad. J. Math. 19 (1967) 1119-1128).

Aleksandrov's proof was topological, based on the concept nowadays called "Alexandrov topology", which is just the order topology derived from the chronology relation in Minkowski space-time. Zeeman's proof, however, was fairly elementary and classical, relying only on bits of analytic geometry. Both the theorem and Zeeman's proof were perfectly within the grasp of the likes of Felix Klein at the time Einstein's work was published, and perfectly within the spirit of Klein's Erlanger Programm as he noticed himself by dismissing special relativity as a simple special case of his programme and calling it the "invariant theory of the Lorentz group" in his address Über die geometrischen Grundlagen der Lorentzgruppe (Jahresbericht der Deutschen Mathematiker-Vereinigung Bd. 19 (1910), pages 533-552 of his collected works). This indicates that he could have proven Zeeman's theorem at least as early as 1910, if only he had the interest.

One example of a missed opportunity, in my opinion, is the Aleksandrov-Zeeman theorem, which states (in one of its different forms) that any bijection of $d$-dimensional Minkowski space-time onto itself ($d>2$) which sends light ray segments into light ray segments (= Einstein's postulate of constancy of the spped of light in Special Relativity) is the composite of one or more of the following:

• A space-time translation;
• A spatial rotation;
• A scale transformation;
• A time reflection;
• A space reflection;
• And a Lorentz boost.

Particularly, this singles out Lorentz boosts as the only transformation law between inertial space-time frames obeying Einstein's postulate. Einstein did show that Lorentz boosts satisfy the latter, but he did not prove whether Lorentz boosts are unique in the above sense, neither did any of his predecessors (Lorentz, Poincaré). Surprisingly, the answer came only about half a century later, through the work of A.D. Aleksandrov in the 50's (assuming the bijection acts linearly) and independently by E.C. Zeeman in 1964 (Causality Implies the Lorentz Group, J. Math. Phys. 5 (1964) 490-493). Aleksandrov dropped the hypothesis of linearity from his argument in 1967 (A Contribution to Chronogeometry, Canad. J. Math. 19 (1967) 1119-1128).

Aleksandrov's proof was topological, based on the concept nowadays called "Alexandrov topology", which is just the order topology derived from the chronology relation in Minkowski space-time. Zeeman's proof, however, was fairly elementary and classical, relying only on bits of analytic geometry. Both the theorem and Zeeman's proof were perfectly within the grasp of the likes of Felix Klein at the time Einstein's work was published, and perfectly within the spirit of Klein's Erlanger Programm as he noticed himself by dismissing special relativity as a simple special case of his programme and calling it the "invariant theory of the Lorentz group" in his address Über die geometrischen Grundlagen der Lorentzgruppe (Jahresbericht der Deutschen Mathematiker-Vereinigung Bd. 19 (1910), pages 533-552 of his collected works). This indicates that he could have proven Zeeman's theorem at least as early as 1910, if only he had the interest.

One example of a missed opportunity, in my opinion, is the Aleksandrov-Zeeman theorem, which states (in one of its different forms) that any bijection of $d$-dimensional Minkowski space-time onto itself ($d>2$) which sends light ray segments into light ray segments (= Einstein's postulate of constancy of the spped of light in Special Relativity) is the composite of one or more of the following:

• A space-time translation;
• A spatial rotation;
• A scale transformation;
• A time reflection;
• A space reflection;
• And a Lorentz boost.

Particularly, this singles out Lorentz boosts as the only transformation law between inertial space-time frames obeying Einstein's postulate. Einstein did show that Lorentz boosts satisfies the latter, but he did not prove whether Lorentz boosts are unique in the above sense, neither did any of his predecessors (Lorentz, Poincaré). Surprisingly, the answer came only about half a century later, through the work of A.D. Aleksandrov in the 50's (assuming the bijection acts linearly) and independently by E.C. Zeeman in 1964 (Causality Implies the Lorentz Group, J. Math. Phys. 5 (1964) 490-493). Aleksandrov dropped the hypothesis of linearity from his argument in 1967 (A Contribution to Chronogeometry, Canad. J. Math. 19 (1967) 1119-1128).

Aleksandrov's proof was topological, based on the concept nowadays called "Alexandrov topology", which is just the order topology derived from the chronology relation in Minkowski space-time. Zeeman's proof, however, was fairly elementary and classical, relying only on bits of analytic geometry. Both the theorem and Zeeman's proof were perfectly within the grasp of the likes of Felix Klein at the time Einstein's work was published, and perfectly within the spirit of Klein's Erlanger Programm as he noticed himself by dismissing special relativity as a simple special case of his programme and calling it the "invariant theory of the Lorentz group" in his address Über die geometrischen Grundlagen der Lorentzgruppe (Jahresbericht der Deutschen Mathematiker-Vereinigung Bd. 19 (1910), pages 533-552 of his collected works). This indicates that he could have proven Zeeman's theorem at least as early as 1910, if only he had the interest.

One example of a missed opportunity, in my opinion, is the Aleksandrov-Zeeman theorem, which states (in one of its different forms) that any bijection of $d$-dimensional Minkowski space-time onto itself ($d>2$) which sends light ray segments into light ray segments (= Einstein's postulate of constancy of the spped of light in Special Relativity) is the composite of one or more of the following:

• A space-time translation;
• A spatial rotation;
• A scale transformation;
• A time reflection;
• A space reflection;
• And a Lorentz boost.

Particularly, this singles out Lorentz boosts as the only transformation law between inertial space-time frames obeying Einstein's postulate. Einstein did show that Lorentz boosts satisfy the latter, but he did not prove whether Lorentz boosts are unique in the above sense, neither did any of his predecessors (Lorentz, Poincaré). Surprisingly, the answer came only about half a century later, through the work of A.D. Aleksandrov in the 50's (assuming the bijection acts linearly) and independently by E.C. Zeeman in 1964 (Causality Implies the Lorentz Group, J. Math. Phys. 5 (1964) 490-493). Aleksandrov dropped the hypothesis of linearity from his argument in 1967 (A Contribution to Chronogeometry, Canad. J. Math. 19 (1967) 1119-1128).

Aleksandrov's proof was topological, based on the concept nowadays called "Alexandrov topology", which is just the order topology derived from the chronology relation in Minkowski space-time. Zeeman's proof, however, was fairly elementary and classical, relying only on bits of analytic geometry. Both the theorem and Zeeman's proof were perfectly within the grasp of the likes of Felix Klein at the time Einstein's work was published, and perfectly within the spirit of Klein's Erlanger Programm as he noticed himself by dismissing special relativity as a simple special case of his programme and calling it the "invariant theory of the Lorentz group" in his address Über die geometrischen Grundlagen der Lorentzgruppe (Jahresbericht der Deutschen Mathematiker-Vereinigung Bd. 19 (1910), pages 533-552 of his collected works). This indicates that he could have proven Zeeman's theorem at least as early as 1910, if only he had the interest.