The spin statistics theorem is a fundamental mathematical proof in quantum mechanics that relates the spin of a particle to the particle statistics it obeys. Specifically, it states that subatomic particles with integral values of spin, such as photons and helium-4 atoms, must be described by Bose-Einstein statistics, while subatomic particles with half-integral values of spin, such as electrons and protons, must be described by Fermi-Dirac statistics. In other words, the spin-statistics theorem states that integer spin particles are bosons, while half-integer spin particles are fermions.

The spin-statistics 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. The theorem is important in understanding the behavior of subatomic particles and is a key concept in quantum field theory. However, it is often considered difficult to understand and has been the subject of ongoing research and debate.