The African Institute for Mathematical Sciences (AIMS) (AIMS.ac.za) is a pan-African network of Centres of Excellence for postgraduate training, research and public engagement in the mathematical sciences. Its mission is to enable Africa's brightest students to flourish as independent thinkers, problem solvers and innovators capable of propelling Africa's future scientific, educational and economic self-sufficiency. AIMS was founded in 2003 and has produced more than 1200 graduates, about one third of whom are women. The goal of the Next Einstein Initiative (NEI) is to build 15 Centres of Excellence across Africa by 2023. Of these, six are already operational in Cameroon, Ghana, Rwanda, Senegal, South Africa and Tanzania.