This manifesto has been written as a practical tool and aid for anyone carrying out, managing or influencing mathematical work. It provides insight into how to undertake and develop mathematically-powered products and services in a safe and responsible way. Rather than give a framework of objectives to achieve, we instead introduce a process that can be integrated into the common ways in which mathematical products or services are created, from start to finish. This process helps address the various issues and problems that can arise for the product, the developers, the institution, and for wider society. To do this, we break down the typical procedure of mathematical development into 10 key stages; our "10 pillars for responsible development" which follow a somewhat chronological ordering of the steps, and associated challenges, that frequently occur in mathematical work. Together these 10 pillars cover issues of the entire lifecycle of a mathematical product or service, including the preparatory work required to responsibly start a project, central questions of good technical mathematics and data science, and issues of communication, deployment and follow-up maintenance specifically related to mathematical systems. This manifesto, and the pillars within it, are the culmination of 7 years of work done by us as part of the Cambridge University Ethics in Mathematics Project. These are all tried-and-tested ideas, that we have presented and used in both academic and industrial environments. In our work, we have directly seen that mathematics can be an incredible tool for good in society, but also that without careful consideration it can cause immense harm. We hope that following this manifesto will empower its readers to reduce the risk of undesirable and unwanted consequences of their mathematical work.

33 pages, 1 figure. This is the first version, and we intend to make revisions. Comments and feedback are welcome - please get in touch with us