It is well known that if a complete manifold M has non-positive sectional curvature K, then M is covered by R^n. One may attempt to improve this by asking whether there is a positive constant epsilon which only depends on the dimension n such that if M is a Riemannian n-manifold with Kd^2 < epsilon, then M is covered by R^n (here d, denoting the diameter, is added to form a quantity independent of scaling). It turns out, the answer is no and a counterexample is given by S^3. That is, for every epsilon > 0, there is a metric on S^3 such that Kd^2 < epsilon. By normalizing the curvature to have a maximum of 1, this says that we can give S^3 a metric with curvature bounded above by 1, with diameter as small as we wish. This talk with follow a paper by Buser and Gromoll, which itself arose from a single sentence in a paper by Gromov as well as a letter by Gromov.