2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57834Octonions are introduced through some spin representations. The groups $G_2$, $F_4$ and the $E$ series appear in a natural manner; one way to understand octonions is as the "second coming" of the reals, but with the spinors instead of vectors. Some physical applications in $M$- and $F$-theory as putative "theories of everything" are suggested.To appear in the Galindofest ProceedingsMathematical Physicstext