A knotted surface is irreducible if it does not have a non-spherical unknotted surface as a summand. In this talk, I will survey previous work on irreducible knotted surfaces and then discuss an example of an irreducible knotted real projective plane, which is a counterexample to Kinoshita’s conjecture. This is joint work with Mark Hughes, Maggie Miller, and Gheehyun Nahm.
