The spin-statistics theorem is a fundamental mathematical proof in quantum mechanics that relates the intrinsic spin of a particle to the particle statistics it obeys. Specifically, the theorem states that subatomic particles having integral values of spin (such as photons and helium-4 atoms) must be described by Bose-Einstein statistics, while subatomic particles having half-integral values of spin (such as electrons and protons) must be described by Fermi-Dirac statistics. The theorem applies to all quantum field theories that have special relativity, positive energies of all particles, and Hilbert space with positive norms of all states. An elementary explanation for the spin-statistics theorem cannot be given despite the fact that the theorem is simple to state.