High Quality Content by WIKIPEDIA articles! In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Cahit Arf (1941) when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2. The Arf invariant is the substitute, in characteristic 2, of the discriminant for quadratic forms in characteristic not 2. Arf used his invariant, among others, in his endeavor to classify quadratic forms in characteristic 2.