Gauss sums are fundamental objects in number theory. Qua- dratic Gauss sums were stud- ied by Gauss who gave a simple formula depending only on the argument of the Gauss sums modulo 4. Higher de- gree Gauss sums behave differently. It was conjectured by Kummer that the angles of cubic Gauss sums at prime arguments are not equidistributed, and exhibit a bias towards small angles. This was disproved by Heath-Brown and Patterson in 1979, who showed that cubic Gauss at prime arguments are equidistributed. This was later generalized by Patterson to general nth- order Gauss sums. We explain in this talk what is involved in proving those results, and how we can improve the results of Patterson for the distribu- tion of quartic Gauss sums at prime arguments. This is joint work with A. Dunn (Georgia Tech), A. Hamieh (UNBC) and H. Lin (North- western).