While extensive usage of high-performance computing has been a staple of other scientific and engineering disciplines for some time, research mathematics is one discipline that has heretofore not yet benefited to the same degree. Now, however, with sophisticated mathematical computing tools and environments widely available on desktop computers, a growing number of remarkable new mathematical results are being discovered partly or entirely with the aid of these tools. For many years, researchers have dreamed of a facility that permits one to recognize a numeric constant in terms of the mathematical formula that it satisfies. With the advent of efficient integer relation detection algorithms, that time has arrived. This article briefly discusses the nature of mathematical experiment. It then presents a few instances primarily of our own recent computer aided mathematical discoveries, and sketches the outlook for the future.