I will try to show how o-minimal geometry (as for instance semi-algebraic geometry) provides a vast field of applications to both nonsmooth and smooth optimization using a simple result called the projection formula. This result is the cornerstone of Sard’s theorems, the nonsmooth Łojasiewicz inequality (KL inequality), and a formal subdifferentiation calculus called conservative calculus. These find in turn applications in deterministic and stochastic algorithms, as well as in automatic differentiation, deep learning, or the differentiation of solution mappings.