In 1981, Gromov proved that for every dimension n, there is a constant C(n) such that every compact connected manifold of dimension n with nonnegative sectional curvature has total betti number bounded by C(n). A natural question to ask is: can this be improved to nonnegative ricci curvature? How about positive Ricci curvature? Sha and Yang answered this in a 1988 paper in which they show that the connect sum of any number of S^n x S^m (n, m >=2) carry a metric of positive ricci curvature. I'll give a sketch of their proof of this fact.