In their celebrated work, B. Andrews and J. Clutterbuck proved the fundamental gap (the difference between the first two eigenvalues) conjecture for convex domains in the Euclidean space and conjectured similar results holds for spaces with constant sectional curvature. In several joint works with S.Seto, L. Wang; C. He; and X. Dai, S.Seto, we prove the conjecture for the sphere. Namely for any strictly convex domain in the unit $S^n$ sphere, the gap is $\ge 3\frac{\pi^2}{D^2}$. As in B. Andrews and J. Clutterbuck's work, the key is to prove a super log-concavity of the first eigenfunction.