This is the story of a mathematical theory which was born from the encounter of several fields. Those fields were: Riemannian geometry, gradient flows, information, and optimal transport; and their encounter took place about 15 years ago. A major result of the interaction was the synthetic theory of Ricci curvature bounds, which was formalized around 2005 and now seems to be reaching maturity, after ten years of fast, sustained growth. As the theory is still in rapid evolution, it is often difficult, even for experts, to trace its progress accurately.