In the field of superconductivity, Anderson's theorem states that superconductivity in a conventional superconductor is robust with respect to (non-magnetic) disorder in the host material.
It is named after P. W. Anderson, who discussed this phenomenon in 1959, briefly after BCS theory was introduced.
[1] One consequence of Anderson's theorem is that the critical temperature Tc of a conventional superconductor barely depends on material purity, or more generally on defects.
This concept breaks down in the case of very strong disorder, e.g. close to a superconductor-insulator transition.
In fact, strong suppression of Tc with increasing defect scattering, thus non-validity of Anderson's theorem, is taken as a strong indication for superconductivity being unconventional.