SUMMARY The rapid and widespread adoption of Java has created a demand for reliable and reusable mathematical software components to support the growing number of computationally intensive applications now under development, particularly in science and engineering. In this paper we address practical issues of the Java language and environment which have an effect on numerical library design and development. Benchmarks which illustrate the current levels of performance of key numerical kernels on a variety of Java platforms are presented. Finally, a strategy for the development of a fundamental numerical toolkit for Java is proposed and its current status is described. ©1998 John Wiley & Sons, Ltd.