Fooled by optimality

An occupational hazard of mathematicians is the investigation of objects that are "optimal" in a mathematically precise sense, yet may be far from optimal in practice. This talk will discuss an extreme example of this effect: Gauss-Hermite quadrature on the real line. For large numbers of quadrature points, Gauss-Hermite quadrature is a very poor method of integration, much less efficient than simply truncating the interval and applying Gauss-Legendre quadrature or the periodic trapezoidal rule. We will present a theorem quantifying this difference and explain where the standard notion of optimality has failed.