Many of the tools we develop build depend on core numerical libraries such as FFTW, or more generally ecosystems such as those from netlib or scipy. Whilst in many cases these core libraries are well regarded and used, the need to either run tools in new environments (such as client-side in a web browser or on a mobile device), or with the rise of new challengers to the current Fortran/C/C++ ecosystem, such as Rust, Julia or possibly even Go, means that either these libraries are being ported, or new libraries being written wholesale. This BoF aims to start the conversation around what we can do to ensure these new libraries are trustworthy, by firstly covering some of the experience of the BoF organisers, and then opening up a wider discussion.