The author contends that computers are unprecedented among human inventions in that they are a boon to experimenters and theorists alike. He points out that the power of computers has grown, and their cost has decreased, at a high-exponential rate-over the last 35 years; and the end is not in sight. In the last 33 years supercomputers, currently the most powerful computers, were needed to solve basic problems in a number of scientific fields. The author argues that novel uses of supercomputers need novel mathematics to make effective use of the computing power, underlining the importance of mathematics for science and of science from mathematics. He cautions that at the level of complexity of supercomputing it is not in general possible to get bounds for the errors due to discretizing the model. >