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Article Summaries:
- John Baez’s MathOverflow post asks whether the two well‑known facts about the octonions-(1) the existence of non‑trivial outer automorphisms of order 3 arising from triality, and (2) the existence of non‑trivial inner automorphisms of order 3 defined by certain unit octonions-can be deduced from one another. He reviews Lamont’s 1963 theorem, which characterises when a unit octonion generates an inner automorphism (angles of 0°, ±120°, ±240°) and shows all such automorphisms have order 3. Baez notes that the Moufang identities and the characteristic equation force this order, and wonders if a link to triality, as hinted by Conway and Smith, can provide a mutual derivation.
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