An algebra in which elements a,b of that algebra obey ab = −ba. This means that a obeys the relation a×a=0. These relations are exactly what is needed to describe the wave functions of fermions. In particular, the relation a×a=0 is a mathematical expression of the Pauli exclusion principle. The concept of such an algebra was devised by the German mathematician Hermann Grassmann (1809–77) in 1844.