Mathematics

There are only 4 division algebras, namely the reals, complexes,
quaternions, and octonions. After constructing the octonions and
discussing their basic properties, I will discuss the remarkable role of
the division algebras in several classification schemes: There are 4
Hopf maps, there are 4 dimensions in which classical supersymmetry is
possible, and all symmetry groups (Lie groups) are locally isomorphic to
matrix groups over one of the 4 division algebras.