"Proof surfaced in 1898 that the reals, complex numbers, quaternions and octonions are the only kinds of numbers that can be added, subtracted, multiplied and divided. "

Not true. Any field (in the algebra sense) has these properties. [1]

Quaternions and octnonions also have weirder properties: quaternions are non-commutatve (jk=-kj) and octnonions are non-associative: a(bc) != (ab)c.

I think the article meant these are the only Euclidean Hurwitz algebras [2], which is a far cry from the claim.

[1] https://en.wikipedia.org/wiki/Field_(mathematics) [2] https://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(compositi...