For more on what's different after the octonions, see: https://en.m.wikipedia.org/wiki/Hurwitz%27s_theorem_(composition_algebras) https://en.m.wikipedia.org/wik

For more on what's different after the octonions, see: https://en.m.wikipedia.org/wiki/Hurwitz%27s_theorem_(composition_algebras) https://en.m.wikipedia.org/wiki/Hurwitz%27s_theorem_(composi... It isn't explicitly stated there, but the statement I recall from algebraic topology is that the octonions are the last normes division algebra.