I will introduce some of the work I’ve been doing - and thinking about doing - with my team at Imperial. Our work tries to span circuits, computer architectures, compilers, and algorithm design. I will focus on some of this work with a strong numerical content. After reviewing the changing face of computer architecture, I will describe some opportunities this opens up for numerical analysts, computer scientists, and hardware engineers to work together, as they did so closely in the early days of computing. I will start by describing some of our fairly well established work on automated numerical code refactoring for efficient implementation, before describing some very recent work on efficient arbitrary precision computation of iterative algorithms based on redundant number representations. I hope to interest numerical analysts to work with me on some of these issues and scientific computing experts to explore their potential in large-scale computation.