Edward Witten on Supersymmetry

“SUSY is a unique new symmetry that relates bosons to fermions, in a sense explaining why fermions exist. Relating bosons to fermions also makes it possible to explain the smallness of the Higgs mass, since we do know why the smallness of fermion masses can be natural. So that is at least the germ of how SUSY solves the fine-tuning problem.”

“Supersymmetry is an updating of special relativity to include fermionic as well as bosonic symmetries of spacetime. In developing relativity, Einstein assumed that the spacetime coordinates were bosonic; fermions had not yet been discovered! In supersymmetry the structure of spacetime is enriched by the presence of fermionic as well as bosonic coordinates.”

“... as a very rough analogy, supersymmetric quantum theory is to ordinary quantum theory as differential forms on a manifold are to functions on a manifold. A very large fraction of geometrical applications of quantum field theory found in the eighties and nineties depend on supersymmetry. (Examples include the supersymmetric proofs of the positive energy theorem, the Atiyah-Singer index theorem, and the Morse inequalities, and the quantum field approaches to elliptic cohomology and to Donaldson theory.) ... Surely, if supersymmetry is confirmed in accelerators, mathematical attention will be focussed on this fruitful branch of quantum field theory roughly as the discovery of general relativity focussed attention on Riemannian geometry.”