A theorem of Adolf Hurwitz, published posthumously in 1923.
It classifies finite-dimensional unital real non-associative algebras with a nondegenerate positive-definite quadratic form.
If the quadratic form defines a homomorphism into the positive reals on the nonzero part, the algebra must be isomorphic to the real numbers, the complex numbers, the quaternions, or the octonions — and there are no others.