The kernel discriminant (a nonparametric Bayesian classifier) is appropriate for many scientific tasks because it is highly accurate (it approaches Bayes optimality as you get more data), distribution-free (works for arbitrary data distributions), and it is easy to inject prior domain knowledge into it and interpret what it's doing. Unfortunately, like other highly accurate classifiers, it is computationally infeasible for massive datasets. We present a fast algorithm for performing classification with the kernel discriminant exactly (i.e. without introducing any approximation error). We demonstrate its use for quasar discovery, a problem central to cosmology and astrophysics, tractably using 500K training data and 800K testing data from the Sloan Digital Sky Survey. The resulting catalog of 100K quasars significantly exceeds existing quasar catalogs in both size and quality, opening a number of new scientific possibilities, including the recent empirical confirmation of cosmic magnification which has received wide attention.