The field of high-performance computing has been very successful in enabling an ever-growing number of important scientific applications to be performed on high-end computer systems. Hardware advances, algorithm improvements, parallelization techniques, performance tools and visualization have all played a part. Recently this technology has been applied in novel ways to research problems in mathematics and mathematical physics. In particular, high-precision numerical computations using the "PSLQ" integer relation algorithm, in many instances implemented on highly parallel computer systems, have been used to discover new mathematical formulas and identities not previously known in the literature. One notable example was the discovery a few years ago of a new formula for pi, which has the remarkable property that it permits one to directly calculate binary or hexadecimal digits beginning at an arbitrary starting position. Many other results have recently been found in this manner, particularly in the area of mathematical physics. This talk gives a brief overview of the techniques used and some of the recent results.