Coleman-Mandula Theorem

It states that the universe cannot obey any symmetry apart from the Poincare Symmetries and the internal symmetries specific to each quantum fields. This theorem is under the assumption that all symmetries are quantified by numbers.

However, Supersymmetry postulates that fermions are represented by Grassman Numbers and there could be a mapping from the Grassman Numbers to ordinary numbers creating superpartners for fermions and bosons. This symmetric mapping is called Supersymmetry.