We outline the proof of the gap theorem stating that any ancient solution to the Ricci flow with Perelman's reduced volume whose asymptotic limit is sufficiently close to that. of the Gaussian soliton must be isometric to the Euclidean space for all time. This is the main result of the author's paper (Yo). Here (SN, g 8 N) is the N(> > 1 )-dimensional round sphere with constant curvature 2 ]v. A remarkable fact is that (M, g) can be thought of as an 'oo-dimensional Ricci-flat space' (e.g. [We]).