it is well-known that the ricci flow will generally develop singularities if one flows an arbitrary initial metric. ancient solutions arise as limits of suitable blow-ups as the time approaches the singular time and thus play a central role in understanding the formation of singularities. by the work of hamilton, perelman, brendle, and many others, ancient solutions are now well-understood in two and three dimensions. in higher dimensions, only a few classification results were obtained and many examples were constructed. in this talk, we show that for any dimension $n \geq 4$, every noncompact rotationally symmetric ancient $kappa$-solution to the ricci flow with bounded positive curvature operator must be the bryant soliton, extending a recent result of brendle to higher dimensions. this is joint work with yongjia zhang.