The HSL Mathematical Software Library (https://www.hsl.rl.ac.uk/) started life in 1963 as the Harwell Subroutine Library. It is the world’s oldest mathematical software library to have been in continual use. Over the years, the HSL Library has continually evolved and has been developed and maintained by a small research group of numerical analysts that has been at the Rutherford Appleton Laboratory since 1990. The group’s interests lie in the development of numerical algorithms and their underlying theory and then implementing these algorithms in state-of-the-art software. The focus for many years has been on sparse problems. The HSL Library has been extensively used on a wide range of computing platforms, from supercomputers to modern PCs and laptops. The current version of the HSL Library is still widely used and it remains a highly respected source of software for solving sparse problems. This article celebrates the 60th anniversary by presenting a short historic overview, summarising the key milestones of the HSL Library 1963–2023.